Strong Coupling Gauge Theories in LHC Era

The following sections are included:

• PREFACE

• OPENING ADDRESS

• WORKSHOP ORGANIZATION

• CONTENTS

The combination of Anti-de Sitter space (AdS) methods with light-front (LF) holography provides a remarkably accurate first approximation for the spectra and wavefunctions of meson and baryon light-quark bound states. The resulting bound-state Hamiltonian equation of motion in QCD leads to relativistic light-front wave equations in terms of an invariant impact variable ζ which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti–de Sitter (AdS) space. The eigenvalues give the hadronic spectrum, and the eigenmodes represent the probability distributions of the hadronic constituents at a given scale. A positive-sign confining dilaton background modifying AdS space gives a very good account of meson and baryon spectroscopy and form factors. The light-front holographic mapping of this model also leads to a non-perturbative effective coupling which agrees with the effective charge defined by the Bjorken sum rule and lattice simulations. It displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale ~ 1 GeV. The resulting β-function appears to capture the essential characteristics of the full β-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD.

We discuss some of the latest results concerning the non-Abelian vortices. The first concerns the construction of non-Abelian BPS vortices based on general gauge groups of the form G = G′ × U(1). In particular detailed results about the vortex moduli space have been obtained for G′ = SO(N) or USp(2N). The second result is about the "fractional vortices", i.e., vortices of the minimum winding but having substructures in the tension (or flux) density in the transverse plane. Thirdly, we discuss briefly the monopole-vortex complex.

The high luminosity e⁺e^- collision at the B-factory experiments (Belle/BaBar) have revealed rich spectra of hadron resonances in the charmonium region. Many of the newly found states do not fit to the unfilled level of the conventional spectrum. Some of them are thought to be exotic states, having sub-structure more complex than the quark anti-quark mesons. In fact, Belle has found some states with non-zero electric charge, that require a minimum quark content of . In this paper, we review the present status of studies on such exotic hadrons at the B-factory experiments.

I describe a novel phase structure of cold dense baryonic matter predicted in a hidden local symmetry approach anchored on gauge theory and in a holographic dual approach based on the Sakai-Sugimoto model of string theory. This new phase is populated with baryons with half-instanton quantum number in the gravity sector which is dual to half-skyrmion in gauge sector in which chiral symmetry is restored while light-quark hadrons are in the color-confined phase. It is suggested that such a phase that aries at a density above that of normal nuclear matter and below or at the chiral restoration point can have a drastic influence on the properties of hadrons at high density, in particular on short-distance interactions between nucleons, e.g., multi-body forces at short distance and hadrons – in particular kaons – propagating in a dense medium. Potentially important consequences on the structure of compact stars will be predicted.

We discuss some recent results on a holographic description of QCD on the basis of a configuration in type IIA superstring theory. A special attention is paid to studies of the baryon dynamics in that model. Using the fact that baryons in large N_c QCD should be regarded as a soliton, it is seen that this model reproduces the experimental data quite nicely.

We compute nuclear forces at short distance, by applying gauge/gravity correspondence to large N_c QCD. This talk is based on work in collaboration with T. Sakai and S. Sugimoto.

We develop a previously proposed gauge-invariant method to integrate out infinite towers of vector and axialvector mesons arising as Kaluza-Klein (KK) modes in a class of holographic models of QCD (HQCD). We demonstrate that HQCD can be reduced to the chiral perturbation theory (ChPT) with the hidden local symmetry (HLS) (so-called HLS-ChPT) having only the lowest KK mode identified as the HLS gauge boson, and the Nambu-Goldstone bosons. The terms in the HLS-ChPT are completely determined by integrating out infinite towers of vector/axialvector mesons in HQCD: Effects of higher KK modes are fully included in the coefficients. As an example, we apply our method to the Sakai-Sugimoto model.

We consider the Polyakov loop in finite temperature planar supersymmetric Yang-Mills theory defined on a spatial S³ and in representations where the number of boxes in the Young Tableau k scales so that remains finite in the large N limit. We review the argument that, in the deconfined phase of the gauge theory, and for symmetric representations with row Young tableau, there is a quantum phase transition in the expectation value of the Polyakov loop operator which occurs as the size of the representation is increased.

In this write-up we summarize main results of our recent analyses on the mixing between transverse ρ and a₁ mesons in hot and/or dense matter. We show that the axial-vector meson contributes significantly to the vector spectral function in hot matter through the mixing. In dense baryonic matter, we include a mixing through a set of ωρa₁-type interactions. We show that a clear enhancement of the vector spectral function appears below for small three-momenta of the ρ meson, and thus the vector spectrum exhibits broadening.

We discuss how the existence of the Gribov horizon affects the deep infrared behavior of ghost and gluon propagators of the D-dimensional SU(N) Yang-Mills theory in the Landau gauge. If we use a horizon function in the Gribov-Zwanziger framework to restrict the functional integral to the first Gribov region for avoiding Gribov copies, we can show that the ghost propagator behaves like free, while the gluon propagator is non-vanishing in deep infrared region (the decoupling solution) in harmony with recent results obtained from numerical simulations on lattice, the Schwinger-Dyson equation and the functional renormalization group. This result should be compared with the Gribov prediction that such a restriction leads to the vanishing gluon propagator and enhanced ghost propagator (the scaling solution). We raise some questions on current understanding on the ghost propagator and its implications for quark confinement à la Wilson and color confinement à la Kugo-Ojima.

This talk presents a recent lattice study by JLQCD and TWQCD collaborations on spontaneous breaking of chiral symmetry. To maintain exact chiral symmetry in the zero quark mass limit, we employ the overlap Dirac operator for the dynamical quark action. The numerical cost for the overlap fermions is high but can be reduced by fixing the topological charge of the gauge fields along the Monte Carlo updates. By studying the low-lying eigenvalues of the Dirac operator, which is always UV finite, we confirm the presence of the chiral condensate. Correcting the finite size effects calculated within the chiral perturbation theory, we determine the value of the chiral condensate at a good accuracy.

In the gauge-Higgs unification the 4D Higgs field becomes a part of the extra-dimensional component of the gauge potentials. In the SO(5) × U(1) gauge-Higgs unification in the Randall-Sundrum warped spacetime the electroweak symmetry is dynamically broken through the Hosotani mechanism. The Higgs bosons become absolutely stable, and become the dark matter of the universe. The mass of the Higgs boson is determined from the WMAP data to be about 70 GeV.

We introduce a toy model implementing the proposal of using a custodial symmetry to protect the coupling from large corrections. This "doublet-extended standard model" adds a weak doublet of fermions (including a heavy partner of the top quark) to the particle content of the standard model in order to implement an O(4) × U(1)_X ~ SU(2)_L × SU(2)_R × P_LR × U(1)_X symmetry in the top-quark mass generating sector. This symmetry is softly broken to the gauged SU(2)_L × U(1)_Y electroweak symmetry by a Dirac mass M for the new doublet; adjusting the value of M allows us to explore the range of possibilities between the O(4)-symmetric (M → 0) and standard-model-like (M → ∞) limits.

We present the latest results on searches for the standard and beyond-the-standard model Higgs bosons in proton-antiproton collisions at by the CDF and DØ experiments at the Fermilab Tevatron. No significant excess is observed above the expected background, and the cross section limits for the Higgs bosons are calculated. It is noticed that the standard model Higgs boson in the mass range 163 – 166 GeV/c² is excluded at the 95% C.L.

We introduce a deconstructed model that incorporates both Higgsless and top-color mechanisms. The model alleviates the typical tension in Higgsless models between obtaining the correct top quark mass and keeping Δ_ρ small. It does so by singling out the top quark mass generation as arising from a Yukawa coupling to an effective top-Higgs which develops a small vacuum expectation value, while electroweak symmetry breaking results largely from a Higgsless mechanism. As a result, the heavy partners of the SM fermions can be light enough to be seen at the LHC.

The dynamics with an infrared stable fixed point in the conformal window in QCD like theories with a relatively large number of fermion flavors is reviewed. The emphasis is on the description of a clear signature for the conformal window, which in particular can be useful for lattice computer simulations of these gauge theories.

Higgs boson production by the gluon fusion and its decay into two photons at the LHC are investigated in the context of the gauge-Higgs unification scenario. The qualitative behaviors for these processes in the scenario are quite distinguishable from those of the Standard Model and the universal extra dimension scenario because of the overall sign difference for the effective couplings induced by one-loop corrections through Kaluza-Klein (KK) modes.

The three site Higgsless model has been offered as a benchmark for studying the collider phenomenology of Higgsless models. In this talk, we present how well the three site Higgsless model performs as a general representative of Higgsless models, in describing W_LW_L scattering, and which modifications can make it more representative. We employ general sum rules relating the masses and couplings of the Kaluza-Klein (KK) modes of the gauge fields in continuum and deconstructed Higgsless models as a way to compare the different theories. After comparing the three site Higgsless model to flat and warped continuum Higgsless models, we analyze an extensions of the three site Higgsless model, namely, the Hidden Local Symmetry (HLS) Higgsless model. We demonstrate that W_LW_L scattering in the HLS Higgsless model can very closely approximate scattering in the continuum models, provided that the parameter 'a' is chosen to mimic ρ-meson dominance of ππ scattering in QCD.

I present recent calculations of the hadronic contributions to muon anomalous magnetic moment in holographic QCD, based on gauge/gravity duality. The holographic estimates are compared well with the analysis based on recently revised BaBar measurements of e⁺e^- → π⁺π^- cross-sections and also with other model calculations for the light-by-light scattering contributions.

We discuss a dark matter candidate peculiar in the gauge-Higgs unification scenario.

A multi-fermion interaction model is investigated in a compact spacetime with non-trivial topology and in a weakly curved spacetime. Evaluating the effective potential in the leading order of the 1/N expansion, we show the phase boundary for a discrete chiral symmetry in an arbitrary dimensions, 2 ≤ D < 4.

We replace the Higgs sector of the electroweak gauge SU(2)_L × U(1)_Y model of three fermion families with its numerous free parameters by a horizontal gauge SU(3)_F quantum flavor dynamics with eight flavor gluon fields and one coupling constant h. We suggest that the new strong low momentum dynamics generates spontaneously the masses of its eight flavor gluons, of leptons and quarks, and of the intermediate W and Z bosons. Absence of axial anomalies requires neutrino right-handed electroweak singlets and brings into the model a new non-Abelian global symmetry. Because the crucial test of the model, the reliable computation of the fermion mass spectrum is not available, we briefly discuss the experimental implications of the resulting neutrino sector.

The following sections are included:

• Introduction

• The conformal window and walking

• Lattice studies of the conformal transition

• References

In contrast to the folklore that Technicolor (TC) is a "Higgsless theory", we shall discuss existence of a composite Higgs boson, Techni-Dilaton (TD), a pseudo-Nambu-Goldstone boson of the scale invariance in the Scale-invariant/Walking/Conformal TC (SWC TC) which generates a large anomalous dimension γ_m ≃ 1 in a wide region from the dynamical mass of the techni-fermion all the way up to the intrinsic scale Λ_TC of the SWC TC (analogue of Λ_QCD), where Λ_TC is taken typically as the scale of the Extended TC scale Λ_ETC: Λ_TC ≃ Λ_ETC ~ 10³ TeV (≫ m). All the techni-hadrons have mass on the same order , which in SWC TC is extremely smaller than the intrinsic scale Λ_TC ≃ Λ_ETC, in sharp contrast to QCD where both are of the same order. The mass of TD arises from the non-perturbative scale anomaly associated with the techni-fermion mass generation and is typically 500-600 GeV, even smaller than other techni-hadrons of the same order of , in another contrast to QCD which is believed to have no scalar bound state lighter than other hadrons. We discuss the TD mass in various methods, Gauged NJL model via ladder Schwinger-Dyson (SD) equation, straightforward calculations in the ladder SD/ Bethe-Salpeter equation, and the holographic approach including techni-gluon condensate. The TD may be discovered in LHC.

We summarize the phase diagrams of SU, SO and Sp gauge theories as function of the number of flavors, colors, and matter representation as well as the ones of phenomenologically relevant chiral gauge theories such as the Bars-Yankielowicz and the generalized Georgi-Glashow models. We finally report on the intriguing possibility of the existence of gauge-duals for nonsupersymmetric gauge theories and the impact on their conformal window.

Different mechanisms for the loss of conformality and analytic ansätze for the beta-function of a generic gauge theory are reviewed and the implications on the conformal windows considered.

We present selected new results on chiral symmetry breaking in nearly conformal gauge theories with fermions in the fundamental representation of the SU(3) color gauge group. We found chiral symmetry breaking (χ^SB) for all flavors between N_f = 4 and N_f = 12 with most of the results discussed here for N_f = 4, 8, 12 as we approach the conformal window. To identify χ^SB we apply several methods which include, within the framework of chiral perturbation theory, the analysis of the Goldstone spectrum in the p-regime and the spectrum of the fermion Dirac operator with eigenvalue distributions of random matrix theory in the ε-regime. Chiral condensate enhancement is observed with increasing N_f when the electroweak symmetry breaking scale F is held fixed in technicolor language. Important finite-volume consistency checks from the theoretical understanding of the SU(N_f) rotator spectrum of the δ-regime are discussed. We also consider these gauge theories at N_f = 16 inside the conformal window. Our work on the running coupling is presented separately.

Strongly coupled gauge theories (SCGT's) have been studied theoretically for many decades using numerous techniques. The obvious motivation for these efforts stemmed from a desire to understand the source of the strong nuclear force: Quantum Chromo-dynamics (QCD). Guided by experimental results, theorists generally consider QCD to be a well-understood SCGT. Unfortunately, it is not clear how to extend the lessons learned from QCD to other SCGT's. Particularly urgent motivators for new studies of other SCGT's are the ongoing searches for physics beyond the standard model (BSM) at the Large Hadron Collider (LHC) and the Tevatron. Lattice gauge theory (LGT) is a technique for systematically-improvable calculations in many SCGT's. It has become the standard for non-perturbative calculations in QCD and it is widely believed that it may be useful for study of other SCGT's in the realm of BSM physics. We will discuss the prospects and potential pitfalls for these LGT studies, focusing primarily on the flavor dependence of SU(3) gauge theory.

We analyze the phases of strong interactions in the space of the flavor number N_f, bare coupling g_L, and temperature T by lattice MonteCarlo simulations for two and three unrooted staggered flavors, corresponding to eight and twelve continuum flavors, respectively. We observe a Coulomb-like phase at intermediate lattice couplings which we interpret as the avatar of a continuum conformal theory for N_f = 12. We comment on the possible occurrence of an UVFP associated with the bulk phase transition between the strong coupling lattice phase and the Coulomb-like phase.

QCD with 2 flavours of massless colour-sextet quarks is studied as a theory which might exhibit a range of scales over which the running coupling constant evolves very slowly (walks). We simulate lattice QCD with 2 flavours of sextet staggered quarks to determine whether walks, or if it has an infrared fixed point, making it a conformal field theory. Our initial simulations are performed at finite temperatures T = 1/N_ta (N_t = 4 and N_t = 6), which allows us to identify the scales of confinement and chiral-symmetry breaking from the deconfinement and chiral-symmetry restoring transitions. Unlike QCD with fundamental quarks, these two transitions appear to be well-separated. The change in coupling constants at these transitions between the two different temporal extents N_t, is consistent with these being finite temperature transitions for an asymptotically free theory, which favours walking behaviour. In the deconfined phase, the Wilson Line shows a 3-state signal. Between the confinement and chiral transitions, there is an additional transition where the states with Wilson Lines oriented in the directions of the complex cube roots of unity disorder into a state with a negative Wilson Line.

The electroweak gauge symmetry is allowed to be spontaneously broken by the strongly interacting vector-like gauge dynamics. When the gauge coupling of a theory runs slowly in a wide range of energy scale, the theory is a candidate for walking technicolor. This may open up the possibility that the origin of all masses may be traced back to the gauge theory. We use the Schrödinger functional method to see whether the gauge coupling of 10-flavor QCD "walks" or not. Preliminary result is reported.

We present a non-perturbative study of the running coupling constant in the Twisted Polyakov Loop (TPL) scheme. We investigate how the systematic and statistical errors can be controlled via a feasibility study in SU(3) pure Yang-Mills theory. We show that our method reproduces the perturbative determination of the running coupling in the UV and gives consistent results with the theoretical prediction in the IR. We also present our preliminary results for N_f = 12 QCD.

New strongly-interacting gauge theories are possible Beyond Standard Model candidates. It is essential to determine if a given non-abelian gauge theory is QCD-like or conformal. One way is to calculate the running of the renormalized gauge coupling. We describe a method to do this using Wilson loop ratios measured in lattice simulations. We demonstrate this in SU(3) pure gauge theory and show initial results for dynamical fermions in the fundamental representation.

We present a simple formulation of non-linear supersymmetry where superfields and partnerless fields can coexist. Using this formalism, we propose a supersymmetric Standard Model without the Higgsino as an effective model for the TeV-scale supersymmetry breaking scenario. We also consider an application of the Hidden Local Symmetry in nonlinear supersymmetry, where we can naturally incorporate a spin-two resonance into the theory in a manifestly supersymmetric way. Possible signatures at the LHC experiments are discussed.

The latest status of LHC and the performances of ATLAS and CMS detectors are summarized in the first part. Physics potential to solve the origin of the ElectroWeak Symmetry Breaking is summarized in the 2nd part, focusing especially on two major scenarios, (1) the light Higgs boson plus SUSY and (2) the Strong Coupling Gauge Theory. Both ATLAS and CMS detectors have the excellent potential to discover them, and we can perform crucial test on the ElectroWeak Symmetry Breaking.

In an exact conformal theory there is no particle. The excitations have continuum spectra and are called "unparticles" by Georgi. We consider supersymmetric extensions of the Standard Model with approximate conformal sectors. The conformal symmetry is softly broken in the infrared which generates a gap. However, the spectrum can still have a continuum above the gap if there is no confinement. Using the AdS/CFT correspondence this can be achieved with a soft wall in the warped extra dimension. When supersym-metry is broken the superpartners of the Standard Model particles may simply be a continuum above gap. The collider signals can be quite different from the standard supersymmetric scenarios and the experimental searches for the continuum superpartners can be very challenging.

We analyze the constraints on the the vacuum polarization of the standard model gauge bosons from a minimal set of flavor observables valid for a general class of models of dynamical electroweak symmetry breaking. We will show that the constraints have a strong impact on the self-coupling and masses of the lightest spin-one resonances.

If Lorentz symmetry is violated at high energies, interactions that are usually non-renormalizable can become renormalizable by weighted power counting. The Standard Model admits a CPT invariant, Lorentz violating extension containing two scalar-two fermion interactions (which can explain neutrino masses) and four fermion interactions (which can explain proton decay). Suppressing the elementary scalar fields, we can use a dynamical symmetry breaking mechanism, in the Nambu–Jona-Lasinio spirit, to generate composite Higgs bosons and masses for fermions and gauge bosons. The low-energy effective action is uniquely determined and predicts relations among parameters of the Standard Model, which allows us to make indirect experimental tests of the high-energy Lorentz violation.

We propose a dynamical model with a (2 + 1)-structure of composite Higgs doublets: two nearly degenerate composites of the fourth family quarks t′ and b′, and and a heavier top-Higgs resonance . This model naturally describes both the top quark mass and the electroweak symmetry breaking. Also, a dynamical mechanism providing the quark mass hierarchy can be reflected in the model. The properties of these composites are analyzed in detail.

We analyze the model of the dynamical electroweak symmetry breaking based on the supersymmetrized Nambu–Jona-Lasinio model with holomorphic dimension-five operators. The Minimal Supersymmetric Standard Model is derived as the low energy effective theory with both Higgs superfields as composites. A renormalization group analysis is performed, including the prediction of the Higgs mass range.

We propose a toy model of baryogenesis which applies the 'ratchet mechanism,' used frequently in the theory of biological molecular motors, to a model proposed by Dimopoulos and Susskind.

In this lecture we review recent analysis of the thermodynamic properties of classical black hole and brane solutions in Einstein Gauss-Bonnet (EGB) gravity. Spherically symmetric black hole solutions of EGB gravity in five dimensions have a lower bound for its mass below which the solution fails to exist. As the mass approaches the minimum value the Hawking temperature approaches zero making the configuration semiclassically stable. Uniform black brane solutions defined in a 4+d dimensional space with d compactified torroidal dimensions also have a minimum mass. As the brane approaches the minimum mass the temperature approaches a non zero value making these configurations semiclassically unstable. Unlike these black branes, black holes caged in a compact space would still have a minimum mass and leave stable remnants under evaporation. Such remnants could constitute one of the components of dark matter.

The dimensionless entropy , , of the visible universe, taken as a sphere of radius 50 billion light years with the Earth at its "center", is discussed. An upper limit (10¹¹²), and a lower limit (10¹⁰²), for are introduced. It is suggested that intermediate-mass black holes (IMBHs) constitute all dark matter, and that they dominate .

The three site Higgsless model is a highly-deconstructed Higgsless model with only three sites. In this model, we show that the KK gauge boson mass, KK fermion mass, and the KK gauge boson couplings with light quarks and leptons are severely constrained by the electroweak precision data. Especially we find that perfect fermiphobity of KK gauge boson is ruled out by the precision data. We also compute the flavor dependent chiral logarithmic corrections to the decay . We find that the phenomenological constraints on this model arising from measurements of are relatively mild, requiring only that the heavy Dirac fermion be heavier than 1 TeV or so, and are satisfied automatically in the range of parameters allowed by the electroweak precision data.

We discuss that the deviation of the Kugo-Ojima color confinement parameter u(0) from -1 in the case of quenched lattice simulation and the consistency with -1 in the case of full QCD simulation could be attributed to the boundary condition defined by fermions inside the region of r < 1fm. By using the domain wall fermion propagator in lattice simulation, we show that the chiral symmetry breaking in the infrared can become manifest when one assumes that the left-handed fermion on the left wall and the right-handed fermion on the right wall are correlated by a self-dual gauge field. The relation between the infrared fixed point of the running coupling measured in lattice simulations, the prediction of the BLM renormalization theory, the conformal field theory with use of the t'Hooft anomaly matching condition in non-SUSY supersymmetric theory and the quaternion real condition are discussed.

We study a holographic model dual to walking/conformal technicolor (W/C TC) deforming a hard-wall type of bottom-up setup by including effects from techni-gluon condensation. We calculate masses of (techni-) ρ meson, a₁ meson, and flavor/chiral-singlet scalar meson identified with techni-dilaton (TD)/conformal Higgs boson, as well as the S parameter. It is shown that gluon contributions and large anomalous dimension tend to decrease specifically mass of the TD. In the typical model with S ≃ 0.1, we find m_TD ≃ 600 GeV, while m_ρ, m_a1 ≃ 4TeV.

Using Bloch-Nordsieck approximation fermion propagator in 3-dimensional gauge theory with topological mass is studied. Infrared divergence of Chern-Simon term is soft, which modifies anomalous dimension. In unquenched QCD with 2-component spinor anomalous dimension has fractional value, where order parmeter is divergent.

Casimir energy is calculated for 5D scalar theory in the warped geometry. A new regularization, called sphere lattice regularization, is taken. The regularized configuration is closed-string like. We numerically evaluate Λ(4D UV-cutoff), ω(5D bulk curvature, warp parameter) and T(extra space IR parameter) dependence of Casimir energy. 5D Casimir energy is finitely obtained after the proper renormalization procedure. The warp parameter ωsuffers from the renormalization effect. We examine the cosmological constant problem.

We study spectral properties of two-color QCD with an even number of flavors at high baryon density. We construct the low-energy effective Lagrangian for the Nambu-Goldstone bosons, derive Leutwyler-Smilga-type spectral sum rules and construct a suitable random matrix theory. Our results can in principle be tested in lattice QCD simulations.

We consider two and three flavor Nambu–Jona-Lasinio (NJL) model at finite temperature by using the dimensional regularization. It is known that physical results produced by the NJL model depend on the method of regularization (Fujihara et al. Prog. Theor. Phys. Suppl. 174, 72 (2008), Phys. Rev. D 79, 096008 (2009)). In the dimensional regularization scheme we regard the space-time dimensions as one of the parameters in the effective theory. We obtain the η meson mass and the topological susceptibility in such regularization and compare the results with ones obtained in the cut-off regularization.

We propose a non-perturbative renormalization group method to investigate the dynamical chiral symmetry breaking in general gauge theories. We setup the effective interaction space to contain all possible 4-fermi interactions allowed by the exact chiral symmetry with N_f flavours. The renormalization group beta functions are calculated without assuming the large-N_f or large-N_c dominance. We solve the renormalization group equation with a small bare mass operator and directly evaluate the induced chiral condensate and the effective mass. We study N_f- and N_c-dependence of the chiral breaking scale including the case having the infrared fixed point for the gauge coupling constant. Also we extend our method to the finite temperature case and obtain the critical temperature of the chiral symmetry restoration.

We study the chiral Lagrangian including the vector mesons such as K* and ρ. The one loop corrections to vector form factors including the chiral breaking is studied. Once we obtain the form factors, one can study the hadronic tau decay τ → Kπν and compute the hadronic invariant distribution.

We consider a SUSY breaking model with anomalous U(1) symmetry. We discard R-symmetry and allow non-renormalizable terms for the model. It will be shown that certain class of models, where the number of positively charged fields is larger than that of negatively charged fields, can have meta-stable SUSY breaking vacuum. And we consider moduli stabilization.

We propose a new description of the SU(N) Yang-Mills theory on a lattice, which enables one to explain quark confinement based on the dual superconductivity picture in a gauge independent way. We apply this fomulation to the SU(3) Yang-Mills theory on a lattice. We give preliminary numerical results showing the dominance of the non-Abelian magnetic monopole in the string tension obtained from the Wilson loop in the fundamental representation.

We study general features of thermodynamic quantities and hadron mass spectra in a possible phase where the chiral SU(2)_L × SU(2)_R symmetry is spontaneously broken while its center Z₂ symmetry remains unbroken.

We study the dependence of the "vector" boson masses (mesons with J^P = 1^– and diquark baryons with J^P = 1⁺) on the baryon number density μ_B for two-color QCD. We show the μ_B-dependence signals the phase transition of U(1)_B breaking and it gives information about mixing among "vector" bosons. We also discuss the comparison with lattice data.

A large class of solutions of the background equations for a specific system of D5-branes shows many of the properties of a walking theory. The gauge coupling is almost constant over an intermediate range of energies, the coupling is strong, the theory confines, a condensate forms. We study the Wilson loops and the spectrum of scalar glueballs in these backgrounds, finding quite surprising results. This model, and possibly its extensions, provide a suitable laboratory in which to study the (strongly coupled) properties of walking dynamics, which lies at the core of walking technicolor.

Note from Publisher: This article contains the abstract only.

We study the quark mass dependence of the baryon mass using Bottom- up approach of holographic QCD. We find that nucleon masses are linear to pion mass square and the slope of ground state, Roper state and N(1535) are 0.74 GeV¹, 0.47 GeV¹ and 0.35 GeV¹ respectively. Then we compare our result with Lattice QCD and results of Top-down approach.

Note from Publisher: This article contains the abstract only.

We non-perturbatively study the structure of quasi-fermion in thermal QED/QCD by solving the Dyson-Schwinger equation in the wide range of temperature as well as of coupling constant. The three-peak structure of the quasi-fermion spectrum, suggested by Harada and Nemoto in a chiral invariant linear sigme model, is clearly seen in QED/QCD. Behavior of the decay width as a function of temperature as well as coupling constant shows the clear deviation from the HTL results. Change of the structure across the boundary of chiral phase transition is also studied in detail.

Note from Publisher: This article contains the abstract only.

We study the critical behaviors of holographic superconductors in 2+1 dimensions. We find the temperature dependences of pion decay constants and mass of sigma-mode, and compute their critical exponents.

Note from Publisher: This article contains the abstract only.

LIST OF PARTICIPANTS