We uncover a novel solution of the 't Hooft anomaly matching conditions for QCD. Interestingly in the perturbative regime the new gauge theory, if interpreted as a possible QCD dual, predicts the critical number of flavors above which QCD in the nonperturbative regime, develops an infrared stable fixed point. Remarkably this value is identical to the maximum bound predicted in the nonpertubative regime via the all-orders conjectured beta function for nonsupersymmetric gauge theories.
We treat quantum chromodynamics (QCD) using a set of Dyson-Schwinger equations derived, in differential form, with the Bender-Milton-Savage technique. In this way, we are able to derive the low energy limit that assumes the form of a non-local Nambu-Jona-Lasinio model. The corresponding gap equation is then studied to show that such a model has no free quarks in the low-energy limit.
We study quantum chromodynamics including the two-index symmetric or anti-symmetric quark (QCD(Sym/ASym)) on small $\mathbb{R}^2\times T^2$ with a suitable magnetic flux. We first discuss the 't Hooft anomaly of these theories and claim that discrete chiral symmetry should be spontaneously broken completely to satisfy the anomaly matching condition. The $T^2$ compactification with the magnetic flux preserves the 't Hooft anomaly, and the $2$d effective theory is constrained by the same anomaly of $4$d QCD(Sym/ASym). We demonstrate the spontaneous breakdown of chiral symmetry using the dilute g…
We study the phase diagram of two-flavor massless two-color QCD (QC$_2$D) under the presence of quark chemical potentials and imaginary isospin chemical potentials. At the special point of the imaginary isospin chemical potential, called the isospin Roberge--Weiss (RW) point, two-flavor QC$_2$D enjoys the $\mathbb{Z}_2$ center symmetry that acts on both quark flavors and the Polyakov loop. We find a $\mathbb{Z}_2$ 't Hooft anomaly of this system, which involves the $\mathbb{Z}_2$ center symmetry, the baryon-number symmetry, and the isospin chiral symmetry. Anomaly matching, therefore, constrai…
YM and QCD are known to be renormalizable, but not ultraviolet finite, order by order in perturbation theory. It is a fundamental question as to whether YM or QCD are ultraviolet finite, or only renormalizable, order by order in the large-N 't Hooft or Veneziano expansions. We demonstrate that Renormalization Group and Asymptotic Freedom imply that in 't Hooft large-N expansion the S-matrix in YM is ultraviolet finite, while in both 't Hooft and Veneziano large-N expansions the S-matrix in confining QCD with massless quarks is renormalizable but not ultraviolet finite. By the same argument it …
As a color confinement mechanism, a dual Meissner effect due to Abelian monopoles involved in QCD has been discussed so far in various ways. But still there is an important problem unsolved. It is gauge invariance of the schemes or, in other words, the reason why non-Abelian color confinement is explained by means of the Abelian dual Meissner effect. Here it is shown that a random Abelian method based on the violation of non-Abelian Bianchi identity (VNABI) could prove SU(3) invariance and explain why color-singlets alone can survive in the confinement phase of QCD in the framework of the Abel…
We find clear numerical evidence for a bilinear condensate in three-dimensional QCD in the 't Hooft limit. We use a non-chiral random matrix model to extract the value of the condensate $Σ$ from the low-lying eigenvalues of the massless anti-Hermitian overlap Dirac operator. We estimate $Σ/λ^2 = 0.0042 \pm 0.0004$ in units of the physical 't Hooft coupling.
Recently it has been shown that in two dimensions is possible to add new Lorentz invariant terms built with fractions containing the null vector $n= (1, 1)$. In this work, we have computed the meson spectrum following the 't Hooft model in $QCD_2$ incorporating these new kinds of terms. We found these new terms does not affect the meson spectrum. We have computed the 't Hooft model with a new regulator. We have introduced a gluon mass and we have recovered the 't Hooft result when this parameter is set to zero.
We study an 't Hooft anomaly of massless QCD at finite temperature. With the imaginary baryon chemical potential at the Roberge-Weiss point, there is a $\mathbb{Z}_2$ symmetry which can be used to define confinement. We show the existence of a mixed anomaly between the $\mathbb{Z}_2$ symmetry and the chiral symmetry, which gives a strong relation between confinement and chiral symmetry breaking. The anomaly is a parity anomaly in the QCD Lagrangian reduced to three dimensions. It is reproduced in the chiral Lagrangian by a topological term related to Skyrmion charge, matching the anomaly befor…
We study the domain walls in hot $4$-D $SU(N)$ super Yang-Mills theory and QCD(adj), with $n_f$ Weyl flavors. We find that the $k$-wall worldvolume theory is $2$-D QCD with gauge group $SU(N-k)\times SU(k) \times U(1)$ and Dirac fermions charged under $U(1)$ and transforming in the bi-fundamental representation of the nonabelian factors. We show that the DW theory has a $1$-form $\mathbb Z_{N}^{(1)}$ center symmetry and a $0$-form $\mathbb Z_{2Nn_f}^{dχ}$ discrete chiral symmetry, with a mixed 't Hooft anomaly consistent with bulk/wall anomaly inflow. We argue that $\mathbb Z_{N}^{(1)}$ is bro…
We discuss the lattice formulation of the 't Hooft surface, that is, the two-dimensional surface operator of a dual variable. The 't Hooft surface describes the world sheets of topological vortices. We derive the formulas to calculate the expectation value of the 't Hooft surface in the multiple-charge lattice Abelian Higgs model and in the lattice non-Abelian Higgs model. As the first demonstration of the formula, we compute the intervortex potential in the charge-2 lattice Abelian Higgs model.
We study the analytic properties of the 't Hooft coupling expansion of the beta-function at the leading nontrivial large-$N_f$ order for QED, QCD, Super QED and Super QCD. For each theory, the 't Hooft coupling expansion is convergent. We discover that an analysis of the expansion coefficients to roughly 30 orders is required to establish the radius of convergence accurately, and to characterize the (logarithmic) nature of the first singularity. We study summations of the beta-function expansion at order $1/N_f$, and identify the physical origin of the singularities in terms of iterated bubble…
The two-dimensional QCD in the large $N$ limit, generally referred to as the 't Hooft model, is numerically investigated in the axial gauge in a comprehensive manner. The corresponding Bethe-Salpeter equation for a bound $q\bar{q}$ pair, originally derived by Bars and Green in 1978, was first numerically tackled by Li and collaborators in late 1980s, yet only for the {\it stationary} mesons. In this paper, we make further progress by numerically solving the Bars-Green equation for {\it moving} mesons, ranging from the chiral pion to charmonium. By choosing several different quark masses, we co…
We construct the Faddeev-Kulish asymptotic states in a quantum field theory of electric and magnetic charges. We find that there are two kind of dressings: apart from the well known (electric) Wilson line dressing, there is a magnetic counterpart which can be written as a 't Hooft line operator. The 't Hooft line dressings are charged under the magnetic large gauge transformation (LGT), but are neutral under electric LGT. This is in contrast to the Faddeev-Kulish dressings of electrons, which can be written as a Wilson line operator and are charged under electric LGT but neutral under magnetic…
We study the topologically twisted index of $\mathcal{N}=6$ supersymmetric Chern-Simons matter theory with $U(N)_k \times U(N)_{-k}$ gauge group in the 't Hooft limit, that is, for $N, k \, \to \infty$ with $λ=N/k$ fixed. In the regime where $λ$ is fixed and large we find an analytical expression for the leading order term of the index. The leading term of the index matches precisely the Bekenstein-Hawking entropy of the dual asymptotically AdS$_4$ magnetically charged black holes embedded in IIA supergrvity on AdS$_4\times \mathbb{CP}^3$, after a standard Legendre transformation. We numerical…
We discuss consequences of the 't Hooft anomaly matching condition for Quantum Chromodynamics (QCD) with massless fundamental quarks. We derive the new discrete 't Hooft anomaly of massless QCD for generic numbers of color $N_\mathrm{c}$ and flavor $N_\mathrm{f}$, and an exotic chiral-symmetry broken phase without quark-bilinear condensate is ruled out from possible QCD vacua. We show that the $U(1)_\mathrm{B}$ baryon number symmetry is anomalously broken when the $(\mathbb{Z}_{2N_\mathrm{f}})_\mathrm{A}$ discrete axial symmetry and the flavor symmetry are gauged. In the ordinary chiral symmet…
We consider the $SU(N)$ Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of $p$. We can formulate such a quantum field theory maintaining locality and unitarity, and the model contains both $2π$-periodic scalar and $3$-form gauge fields. This can be interpreted as coupling a topological theory to Yang-Mills theory, so the local dynamics becomes identical with that of pure Yang-Mills theory. The theory has not only $\mathbb{Z}_N$ $1$-form symmetry but also $\mathbb{Z}_p$ $3$-form symmetry, and we study the global nature of this theory fr…
Finite 't Hooft coupling corrections to multiple physical observables in strongly coupled $N=4$ supersymmetric Yang-Mills plasma are examined, in an attempt to assess the stability of the expansion in inverse powers of the 't Hooft coupling $λ$. Observables considered include thermodynamic quantities, transport coefficients, and quasinormal mode frequencies. Although large $λ$ expansions for quasinormal mode frequencies are notably less well behaved than the expansions of other quantities, we find that a partial resummation of higher order corrections can significantly reduce the sensitivity o…
