Center vortex and confinement in Yang-Mills theory and QCD with anomaly-preserving compactifications

Abstract

We construct an anomaly-preserving compactification of 4d gauge theories, including $SU(N)$ Yang-Mills theory, $\mathcal{N}=1$ supersymmetric Yang-Mills theory, and QCD, down to 2d by turning on 't Hooft flux through $T^2$. It provides a new framework to analytically calculate nonperturbative properties such as confinement, chiral symmetry breaking, and multi-branch structure of vacua. We give the semiclassical description of these phenomena based on the center vortex and show that it enjoys the same anomaly matching condition with the original $4$d gauge theory. We conjecture that the weak-coupling vacuum structure on small $T^2\times {\mathbb{R}}^2$ is adiabatically connected to the strong-coupling regime on ${\mathbb{R}}^4$ without any phase transitions. In QCD with fundamental quarks as well, we can turn on 't Hooft flux either by activating $SU(N_f{)}_{\mathrm{V}}$ symmetry twist for $N_f=N$ flavors or by introducing a magnetic flux of baryon number $U(1{)}_{\mathrm{B}}$ for arbitrary $N_f$ flavors. In both cases, the weak-coupling center-vortex theory gives the prediction consistent with chiral Lagrangian of $4$d QCD.

58 pages, 5 figures (v2) minor changes

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Cited by in corpus (16)

• Semiclassics with 't Hooft flux background for QCD with $2$-index quarks
• Unifying Monopole and Center Vortex as the Semiclassical Confinement Mechanism
• Higher Berry Phase of Fermions and Index Theorem
• Semiclassical analysis of the bifundamental QCD on ${\mathbb{R}}^2\times T^2$ with 't Hooft flux
• Topology of $SU(N)$ lattice gauge theories coupled with ${\mathbb{Z}}_N$ $2$-form gauge fields
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• Symmetry Transmutation and Anomaly Matching
• Monopole-vortex continuity of $\mathcal{N}=1$ super Yang-Mills theory on ${\mathbb{R}}^2\times S^1\times S^1$ with 't Hooft twist
• Winding theta and destructive interference of instantons
• Note on lattice description of generalized symmetries in $SU(N)/{\mathbb{Z}}_N$ gauge theories
• ${\mathbb{Z}}_N$ stability and continuity in twisted Eguchi-Kawai model with two-flavor adjoint fermions
• Center-vortex semiclassics with non-minimal 't Hooft fluxes on ${\mathbb{R}}^2\times T^2$ and center stabilization at large $N$
• ${\mathbb{Z}}_3$ lattice gauge theory as a toy model for dense QCD
• Novel first-order phase transition and critical points in SU(3) Yang-Mills theory with spatial compactification
• Large $\theta$ angle in two-dimensional large $N$ ${\mathbb{CP}}^{N-1}$ model
• Topology of Calorons Re-examined