Narrow Results

We analyze a beta function with the analytic form of Novikov–Shifman–Vainshtein–Zakharov result in the five-dimensional gravity-dilaton environment. We show how dilaton inherits poles and fixed points of such beta function through the zeros and points of extremum in its potential. Super Yang–Mills and supersymmetric QCD are studied in detail and Seiberg's electric-magnetic duality in the dilaton potential is explicitly demonstrated. Non-supersymmetric proposals of similar functional form are tested and new insights into the conformal window as well as determinations of scheme-independent value of the anomalous dimension at the fixed point are presented.

We consider zero-temperature transitions from conformal to non-conformal phases in quantum theories. We argue that there are three generic mechanisms for the loss of conformality: (i) fixed point goes to zero coupling, (ii) fixed point runs off to infinite coupling, or (iii) an IR fixed point annihilates with a UV fixed point and they both disappear into the complex plane. We give examples of the last case and show that the critical behavior of the mass gap is similar to that of the inverse correlation length in the finite temperature Berezinskii-Kosterlitz-Thouless (BKT) phase transition, ξ ~ exp(c/|T-T_c|^1/2). We speculate that the chiral phase transition in QCD at large number of fermion flavors belongs to this universality class, and attempt to identify the UV fixed point that annihilates with the Banks-Zaks fixed point at the lower end of the conformal window.

We investigate the gauge dynamics of nonsupersymmetric SU(N) gauge theories featuring the simultaneous presence of fermionic matter transforming according to two distinct representations of the underlying gauge group. We bound the regions of flavors and colors which can yield a physical infrared fixed point. As a consistency check we recover the previously investigated bounds of the conformal windows when restricting to a single matter representation. The earlier conformal windows can be imagined to be part now of the new conformal house. We predict the nonperturbative anomalous dimensions at the infrared fixed points. We further investigate the effects of adding mass terms to the condensates on the conformal house chiral dynamics and construct the simplest instanton induced effective Lagrangian terms.

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.

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 ≡ N_f/N_c. In particular, we review the results for the S-parameter, the technidilaton, and the masses of the mesons.

We consider zero-temperature transitions from conformal to non-conformal phases in quantum theories. We argue that there are three generic mechanisms for the loss of conformality: (i) fixed point goes to zero coupling, (ii) fixed point runs off to infinite coupling, or (iii) an IR fixed point annihilates with a UV fixed point and they both disappear into the complex plane. We give examples of the last case and show that the critical behavior of the mass gap is similar to that of the inverse correlation length in the finite temperature Berezinskii-Kosterlitz-Thouless (BKT) phase transition, ξ ~ exp(c/|T - T_c|^1/2). We speculate that the chiral phase transition in QCD at large number of fermion flavors belongs to this universality class, and attempt to identify the UV fixed point that annihilates with the Banks-Zaks fixed point at the lower end of the 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 discuss various aspects of Conformal Field Theories on the Lattice. We mainly investigate the SU(3) gauge theory with N_f degenerate fermions in the fundamental representation, employing the one-plaquette gauge action and the Wilson fermion action.

First we make a brief review of our previous works on the phase structure of lattice gauge theories in terms of the gauge coupling constant and the quark mass. We thereby clarify the reason why we conjecture that the conformal window is 7 ≤ N_f ≤ 16.

Secondly, we introduce a new concept, “conformal theories with IR cutof” and point out that any numerical simulation on a lattice is bounded by an IR cutoff ∧_IR. Then we make predictions that when N_f is within the conformal window, the propagator of a meson G(t) behaves at large t, as G(t) = c exp (−m_Ht)/t^α, that is, a modified Yukawa-type decay form, instead of the usual exponential decay form exp (−m_Ht), in the small quark mass region. This holds on an any lattice for any coupling constant g, as far as g is between 0 and g*, where g* is the IR fixed point. We verify that numerical results really satisfy the predictions for the N_f = 7 case and the N_f = 16 case.

Thirdly, we discuss small number of flavors (N_f = 2 ∼ 6) QCD at finite temperatures. We point out theoretically and verify numerically that the correlation functions at T/T_c > 1 exhibit the characteristics of the conformal function with IR cutoff, an exponential decay with power correction.

Investigating our numerical data by a new method which we call the “local-analysis” of propagators, we observe that the N_f = 7 case and the N_f = 2 at T ∼ 2T_c case are similar to each other, while the N_f = 16 case and the N_f = 2 at T = 10² ∼ 10⁵T_c cases are similar to each other.

Further, we observe our data are consistent with the picture that the N_f = 7 case and the N_f = 2 at T ∼ 2T_c case are close to the meson unparticle model. On the other hand, the N_f = 16 case and the N_f = 2 at T = 10² ∼ 10⁵T_c cases are close to a free state in the Z(3) twisted vacuum. All results are consistent with naive physical intuition and give clues for long standing issues at high temperatures such as why the free energy at high temperatures does not reach the Stefan-Boltzmann ideal gas limit even at T = 100T_c.

We study infrared conformality of the twelve-flavor QCD on the lattice. Utilizing a HISQ type action which is useful to study the continuum physics, we analyze the lattice data of the mass and the decay constant of a pseudoscalar meson and the mass of a vector meson as well at several values of lattice spacing and fermion mass. Our result is consistent with the conformal hypothesis for the mass anomalous dimension γ_m ∼ 0.4 – 0.5.

It is well known that the SU(3) gauge theory with the fundamental 16-flavor fermion is governed by a non-trivial infrared fixed point in the 2-loop perturbation theory, while the theory has not been well investigated by non-perturbative lattice gauge simulations. We investigate properties of 16-flavor QCD by lattice simulation with highly improved actions(HISQ/tree) at wide range of the lattice spacing. We present the Polyakov loop in the spatial direction at several values of β at fixed lattice size and fermion mass. From the result we find that the finite size effect might be large at β = 12, where the lattice bare coupling is almost same as the coupling at the perturbative fixed point. We discuss the finite-size hyperscaling of the mass of pseudoscalar meson to estimate the mass anomalous dimension γ, while the results might have large finite size effect. It is encouraging that the estimated γ is consistent with the perturbative value, although our estimate has large uncertainty.