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

Anber, Mohamed M. and Poppitz, Erich (2019) 'Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj).', Journal of high energy physics., 2019 (5). p. 151.


We study the domain walls in hot 4-D SU(N) super Yang-Mills theory and QCD(adj), with nf 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 Zdχ2Nnf 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 Zdχ2Nnf is also broken f 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.

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Publisher statement:Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
Date accepted:07 May 2019
Date deposited:04 October 2021
Date of first online publication:23 May 2019
Date first made open access:04 October 2021

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