Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj)

Abstract

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) × SU (k) × 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 Z(1) N center symmetry and a 0-form Z dχ 2N n f discrete chiral symmetry, with a mixed 't Hooft anomaly consistent with bulk/wall anomaly inflow. We argue that Z (1) N is broken on the wall, and hence, Wilson loops obey the perimeter law. The breaking of the worldvolume center symmetry implies that bulk p-strings can end on the wall, a phenomenon first discovered using string-theoretic constructions. We invoke 2-D bosonization and gauged Wess-Zumino-Witten models to suggest that Z dχ 2N n f is also broken in the IR, which implies that the 0-form/1-form mixed 't Hooft anomaly in the gapped k-wall theory is saturated by a topological quantum field theory. We also find interesting parallels between the physics of high-temperature domain walls studied here and domain walls between chiral symmetry breaking vacua in the zero temperature phase of the theory (studied earlier in the semiclassically calculable small spatial circle regime), arising from the similar mode of saturation of the relevant 't Hooft anomalies.2 These do not yield to controlled analytic studies, but require lattice simulations or model assumptions [1]. 3 Many of these studies focused on the k-wall tension, argued to exhibit Casimir scaling as in (2.11). 4 The "dχ" superscript is a reminder of the nature of the discrete symmetry. 5 These calculable compactifications are in many cases continuously connected to the R 4 strongly coupled theory, see [28] for a recent review and references. 7 More precisely, the k-wall worldvolume gauge group is SU (N − k) × SU (k) × U (1)/(Z N −k × Z k ).

Generalized ’t Hooft anomalies on non-spin manifolds

“…Constructing the IR TQFTs that must accompany the various exotic phases mentioned here is also of interest (we also note that their UV origin remains mysterious). Anomalies should also have implications for the finite temperature phase structure, as in [5,7,[50][51][52].…”

Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow

“…The mixed 0-form/1form anomalies imply that in theories with such anomalies, DWs occurring due to 0-form discrete symmetry breaking have a nontrivial structure on their worldvolume. Such DWs have recently received some attention [27][28][29][30][31][32][33][34][35][36]. The nontrivial DW physics is usually described in terms of a topological quantum field theory (TQFT) living on the DW, e.g.…”

“…A different way to describe the N k = 1 walls is in terms of a worldvolume TQFT. 18 It was suggested in [31] that the worldvolume theory is the Z N 2d topological gauge theory…”

Lattice gauge theory for the Haldane conjecture and central-branch Wilson fermion

“…In the continuum, we can consider the U (1) gauge theory only with charge-q Dirac fermions, which leads to the larger discrete chiral symmetry, Z2q [31][32][33]37] (see also [58,59]). However, due to the fact that we have an on-site U (1) symmetry that can be gauged as charge-1 theory, we can only have Z2 chiral symmetry in our lattice construction when we consider no fine-tuning.…”

“…is invariant. This mass term is given by 32) and this breaks the site-dependent U (1) symmetry, U (1) V . We note that the flavored mass, introduced in Refs.…”