International Journal of Modern Physics A

First, we give a gauge-independent definition of chromomagnetic monopoles in $SU(N)$ Yang–Mills theory which is derived through a non-Abelian Stokes theorem for the Wilson loop operator. Then we discuss how such magnetic monopoles can give a nontrivial contribution to the Wilson loop operator for understanding the area law of the Wilson loop average. Next, we discuss how the magnetic monopole condensation picture are compatible with the vortex condensation picture as another promising scenario for quark confinement. We analyze the profile function of the magnetic flux tube as the non-Abelian vortex solution of $U(N)$ gauge-Higgs model, which is to be compared with numerical simulations of the $SU(N)$ Yang–Mills theory on a lattice. This analysis gives an estimate of the string tension based on the vortex condensation picture, and possible interactions between two non-Abelian vortices.

In the preceeding works, we have given a non-Abelian dual superconductivity picture for quark confinement, and demonstrated the numerical evidences on the lattice. In this talk, we discuss the confinement and deconfinement phase transition at finite temperature in view of the dual superconductivity. We investigate chromomagnetic monopole currents induced by chromoelectric flux in both confinement and deconfinement phase by the numerical simulations on a lattice at finite temperature, and discuss the role of the chromomagnetic monopole in the confinement/deconfinement phase transition.

We discuss holographic QCD in the Veneziano limit (the V-QCD models), concentrating on phenomena near the “conformal” phase transition taking place at a critical value of the ratio $x\equiv N_f/N_c$. In particular, we review the results for the S-parameter, the technidilaton, and the masses of the mesons.

The duality conjecture states that $p+1$-dimensional maximally supersymmetric Yang–Mills theory at finite temperature is expected to be dual to the non extremal black $p$-brane at large N. We perform the lattice simulations of SYM for $p=0,1$ to investigate the validity of the conjecture. We show that the conjecture is qualitatively valid by comparing lattice results of the black $p$-branes mass with analytic expectations in the gravity side.

We summarize recent progress in lattice studies of four-dimensional ${𝒩}=4$ supersymmetric Yang–Mills theory and present preliminary results from ongoing investigations. Our work is based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, and we review a new procedure to regulate flat directions by modifying the moduli equations in a manner compatible with this supersymmetry. This procedure defines an improved lattice action that we have begun to use in numerical calculations. We discuss some highlights of these investigations, including the static potential and an update on the question of a possible sign problem in the lattice theory.

We discuss a new mechanism of D-term dynamical supersymmetry breaking in the context of Dirac gaugino scenario. The existence of a nontrivial solution of the gap equation for D-term is shown. It is also shown that an observed 126 GeV Higgs mass is realized by tree level D-term effects in a broad range of parameters.

We explore the generation of large-scale magnetic fields in the so-called moduli inflation. The hypercharge electromagnetic fields couple to not only a scalar field but also a pseudoscalar one, so that the conformal invariance of the hypercharge electromagnetic fields can be broken. We explicitly analyze the strength of the magnetic fields on the Hubble horizon scale at the present time, the local non-Gaussianity of the curvature perturbations originating from the massive gauge fields, and the tensor-to-scalar ratio of the density perturbations. As a consequence, we find that the local non-Gaussianity and the tensor-to-scalar ratio are compatible with the recent Planck results.

A new heavy di-jet resonance could be discovered at the 14 TeV LHC. In this talk we present a strategy to reveal the nature of such a particle; in particular to discern whether it is a quark–antiquark $(q\bar{q})$, quark–gluon $(qg)$, or gluon–gluon $(gg)$ resonance. The strategy is based on the study of the energy profiles of the two leading jets in the di-jet channel. Including statistical uncertainties in the signal and the QCD backgrounds, we show that one can distinguish between $gg$, $qg$, and $q\bar{q}$ resonances; an evaluation of systematic uncertainties in the measurement of the jet energy profile will require a detailed detector study once sufficient 14 TeV di-jet data is in hand.

Color-singlet and color-octet vector bosons predicted in theories beyond the Standard Model have the potential to be discovered as dijet resonances at the LHC. A color-singlet resonance that has leptophobic couplings needs further investigation to be distinguished from a color-octet one. In previous work, we introduced a method for discriminating between the two kinds of resonances when their couplings are flavor-universal, using measurements of the dijet resonance mass, total decay width and production cross-section. Here, we describe two extensions of that work. First, we broaden the method to the case where the vector resonances have flavor non-universal couplings, by incorporating measurements of the heavy-flavor decays of the resonance. Second, we apply the method to separating vector bosons from color-octet scalars and excited quarks.

We apply the orbifold grand unified theory (GUT) mechanism to the noncommutative Higgs model. An assignment of $Z_2$ parity to the “constituent fields” induces parity assignments of both the gauge and Higgs bosons, because these bosons are treated as some kind of composite fields in this formalism.

We discuss properties of non-Abelian gauge theories that change significantly across the lower edge of the conformal window. Their probes are the topological observables, the meson spectrum and the scalar glueball operator. The way these quantities change tells about the way conformal symmetry is lost.

The first Nagoya SCGT workshop back in 1988 (SCGT 88) was motivated by the walking technicolor and technidilaton. Now at SCGT15 I returned to the “old wine” in “a new bottle”, the recently discovered 125 Higgs boson as the technidilaton. We show that the Standard Model (SM) Higgs Lagrangian is identical to the nonlinear realization of both the scale and chiral symmetries (“scale-invariant nonlinear sigma model”), and is further gauge equivalent to the “scale-invariant Hidden Local Symmetry (HLS) model” having possible new vector bosons as the HLS gauge bosons with scale-invariant mass: SM Higgs is nothing but a (pseudo) dilaton. The effective theory of the walking technicolor has precisely the same type of the scale-invariant nonlinear sigma model, thus further having the scale-invariant HLS gauge bosons (technirho’s, etc.). The technidilaton mass $M_{\varphi }$ comes from the trace anomaly, which yields $M_{\varphi }^2{F}_{\varphi }^2\simeq [\frac{8}{N_F}\frac{4}{N_C}]\cdot {(2.5)}^2\cdot v^4$ via PCDC, in the underlying walking $SU(N_C)$ gauge theory with $N_F$ massless flavors, where $F_{\varphi }$ is the the decay constant and $v=246\mathrm{\text{GeV}}$. This implies $F_{\varphi }\simeq 5v$ for $M_{\varphi }\simeq 125\mathrm{\text{GeV}}\simeq \frac{1}{2}v$ in the one-family walking technicolor model $(N_C=4,N_F=8)$, in good agreement with the current LHC Higgs data. In the anti-Veneziano limit, $N_C\to \infty$, with $N_C\alpha =$fixed and $N_F/N_C=$fixed $(\gg 1)$, we have a result: $M_{\varphi }^2/v^2\sim M_{\varphi }^2/F_{\varphi }^2\sim 1/(N_F{N}_C)\to 0$. Then the technidilaton is a naturally light composite Higgs out of the strongly coupled conformal dynamics, with its couplings even weaker than the SM Higgs. Related holographic and lattice results are also discussed. In particular, such a light flavor-singlet scalar does exists in the lattice simulations in the walking regime.

In this brief talk, I will try to focus on the things that happened at the conference that seemed very important, but that I didn’t understand.

We construct a simple model for describing the hadron–quark crossover transition by using lattice QCD (LQCD) data in the $2+1$ flavor system, and draw the phase diagram in the $2+1$ and $2+1+1$ flavor systems through analyses of the equation of state (EoS) and the susceptibilities. In the present hadron–quark crossover (HQC) model, the entropy density $s$ is defined by $s=f_{\mathrm{\text{H}}}{s}_{\mathrm{\text{H}}}+(1-f_{\mathrm{\text{H}}})s_{\mathrm{\text{Q}}}$ with the hadron-production probability $f_{\mathrm{\text{H}}}$, where $s_{\mathrm{\text{H}}}$ is calculated by the hadron resonance gas model that is valid in low temperature $(T)$ and $s_{\mathrm{\text{Q}}}$ is evaluated by the independent quark model that explains LQCD data on the EoS in the region $400\lesssim T\le 500\mathrm{\text{MeV}}$ for the $2+1$ flavor system and $400\lesssim T\le 1000\mathrm{\text{MeV}}$ for the $2+1+1$ flavor system. The $f_{\mathrm{\text{H}}}$ is determined from LQCD data on $s$ and susceptibilities for the baryon-number $(B)$, the isospin $(I)$ and the hypercharge $(Y)$ in the $2+1$ flavor system. The HQC model is successful in reproducing LQCD data on the EoS and the flavor susceptibilities ${\chi }_{f{f}^{\prime }}^{(2)}$ for $f$, $f^{\prime }=\mathrm{\text{u}}$, $\mathrm{\text{d}}$, $\mathrm{\text{s}}$ in the $2+1+1$ flavor system, without changing the $f_{\mathrm{\text{H}}}$. We define the hadron–quark transition temperature with $f_{\mathrm{\text{H}}}=1/2$. For the $2+1$ flavor system, the transition line thus obtained is almost identical in ${\mu }_B\text{–}T$, ${\mu }_I\text{–}T$, ${\mu }_Y\text{–}T$ planes, when the chemical potentials ${\mu }_{\alpha }$ $(\alpha =B,I,Y)$ are smaller than 250 MeV. This $BIY$ approximate equivalence is also seen in the $2+1+1$ flavor system. We plot the phase diagram also in ${\mu }_{\mathrm{\text{u}}}\text{–}T$, ${\mu }_{\mathrm{\text{d}}}\text{–}T$, ${\mu }_{\mathrm{\text{s}}}\text{–}T$, ${\mu }_{\mathrm{\text{c}}}\text{–}T$ planes in order to investigate flavor dependence of transition lines. In the $2+1+1$ flavor system, $\mathrm{\text{c}}$ quark does not affect the $2+1$ flavor subsystem composed of $\mathrm{\text{u}}$, $\mathrm{\text{d}}$, $\mathrm{\text{s}}$. Temperature dependence of the off-diagonal susceptibilities and the $f_{\mathrm{\text{H}}}$ show that the transition region at ${\mu }_{\alpha }=0$ is $170\lesssim T\lesssim 400\mathrm{\text{MeV}}$ for both the $2+1$ and $2+1+1$ flavor systems.

The nonrelativistic covariant framework for fields is extended to investigate fields and fluids on scale covariant curved backgrounds. The scale covariant Newton–Cartan background is constructed using the localization of space–time symmetries of nonrelativistic fields in flat space. Following this, we provide a Weyl covariant formalism which can be used to study scale invariant fluids. By considering ideal fluids as an example, we describe its thermodynamic and hydrodynamic properties and explicitly demonstrate that it satisfies the local second law of thermodynamics. As a further application, we consider the low energy description of Hall fluids. Specifically, we find that the gauge fields for scale transformations lead to corrections of the Wen–Zee and Berry phase terms contained in the effective action.

We study the most general renormalizable couplings containing Higgs $H(10)$, $D(120)$, $\bar{\mathrm{\Delta }}(\overline{126})+\mathrm{\Delta }(126)$, $A(45)$, $E(54)$ and $\mathrm{\Phi }(210)$ in the supersymmetric SO(10) models. The Clebsch–Gordan coefficients are calculated using the maximal subgroup $\mathrm{\text{SU}}(5)\times \mathrm{\text{U}}{(1)}_X$.

Fermion production in external electric field on de Sitter expanding universe is analyzed. The amplitude and probability of pair production are computed. We obtain from our calculations that the modulus of the momentum is no longer conserved. The rate of pair production in an electric field is found to be important in the early universe when the expansion factor was large comparatively with the particle mass. A computation of the total probability is presented in a particular case and the result proves to be nonvanishing only in strong gravitational fields.

In this paper, we bring out the subtleties involved in the study of a first-order relativistic field theory with auxiliary field variables playing an essential role. In particular, we discuss the nonisentropic Eulerian (or Hamiltonian) fluid model. Interactions are introduced by coupling the fluid to a dynamical Maxwell (U(1)) gauge field. This dynamical nature of the gauge field is crucial in showing the equivalence, on the physical subspace, of the stress tensor derived from two definitions, i.e. the canonical (Noether) one and the symmetric one. In the conventional equal-time formalism, we have shown that the generators of the space–time transformations obtained from these two definitions agree modulo the Gauss constraint. This equivalence in the physical sector has been achieved only because of the dynamical nature of the gauge fields. Subsequently, we have explicitly demonstrated the validity of the Schwinger condition. A detailed analysis of the model in lightcone formalism has also been done where several interesting features are revealed.