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Title: Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD

Abstract

We show that 2 2 d adjoint QCD, an SU(N) S U ( N ) gauge theory with one massless adjoint Majorana fermion, has a variety of mixed ’t Hooft anomalies. The anomalies are derived using a recent mod 2 2 index theorem and its generalization that incorporates ’t Hooft flux. Anomaly matching and dynamical considerations are used to determine the ground-state structure of the theory. The anomalies, which are present for most values of N N , are matched by spontaneous chiral symmetry breaking. We find that massless 2 2 d adjoint QCD confines for N >2 N > 2 , except for test charges of N N -ality N/2 N / 2 , which are deconfined. In other words, \mathbb Z_N N center symmetry is unbroken for odd N N and spontaneously broken to \mathbb Z_{N/2} N / 2 for even N N . All of these results are confirmed by explicit calculations on small \mathbb{R}\times S^1 × S 1 . We also show that this non-supersymmetric theory exhibits exact Bose-Fermi degeneracies for all states, including the vacua, when N N is even. Furthermore, for most values of N N , 2 2 d massive adjoint QCD describes a non-trivial symmetry-protected topological (SPT) phase of matter, including certain cases where the number of interacting Majorana fermions is a multiple of 8 8 . As a result, it fits into the classification of (1+1) ( 1 + 1 ) d SPT phases of interacting Majorana fermions in an interesting way.

Authors:
 [1];  [1];  [2];  [3]
  1. University of Minnesota
  2. Kyoto University, North Carolina State University
  3. North Carolina State University
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1617245
Grant/Contract Number:  
FG02-03ER41260
Resource Type:
Published Article
Journal Name:
SciPost Physics Proceedings
Additional Journal Information:
Journal Name: SciPost Physics Proceedings Journal Volume: 8 Journal Issue: 5; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English

Citation Formats

Cherman, Aleksey, Jacobson, Theo, Tanizaki, Yuya, and Ünsal, Mithat. Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD. Netherlands: N. p., 2020. Web. doi:10.21468/SciPostPhys.8.5.072.
Cherman, Aleksey, Jacobson, Theo, Tanizaki, Yuya, & Ünsal, Mithat. Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD. Netherlands. doi:https://doi.org/10.21468/SciPostPhys.8.5.072
Cherman, Aleksey, Jacobson, Theo, Tanizaki, Yuya, and Ünsal, Mithat. Tue . "Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD". Netherlands. doi:https://doi.org/10.21468/SciPostPhys.8.5.072.
@article{osti_1617245,
title = {Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD},
author = {Cherman, Aleksey and Jacobson, Theo and Tanizaki, Yuya and Ünsal, Mithat},
abstractNote = {We show that 2 2 d adjoint QCD, an SU(N) S U ( N ) gauge theory with one massless adjoint Majorana fermion, has a variety of mixed ’t Hooft anomalies. The anomalies are derived using a recent mod 2 2 index theorem and its generalization that incorporates ’t Hooft flux. Anomaly matching and dynamical considerations are used to determine the ground-state structure of the theory. The anomalies, which are present for most values of N N , are matched by spontaneous chiral symmetry breaking. We find that massless 2 2 d adjoint QCD confines for N >2 N > 2 , except for test charges of N N -ality N/2 N / 2 , which are deconfined. In other words, \mathbb Z_N ℤ N center symmetry is unbroken for odd N N and spontaneously broken to \mathbb Z_{N/2} ℤ N / 2 for even N N . All of these results are confirmed by explicit calculations on small \mathbb{R}\times S^1 ℝ × S 1 . We also show that this non-supersymmetric theory exhibits exact Bose-Fermi degeneracies for all states, including the vacua, when N N is even. Furthermore, for most values of N N , 2 2 d massive adjoint QCD describes a non-trivial symmetry-protected topological (SPT) phase of matter, including certain cases where the number of interacting Majorana fermions is a multiple of 8 8 . As a result, it fits into the classification of (1+1) ( 1 + 1 ) d SPT phases of interacting Majorana fermions in an interesting way.},
doi = {10.21468/SciPostPhys.8.5.072},
journal = {SciPost Physics Proceedings},
number = 5,
volume = 8,
place = {Netherlands},
year = {2020},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
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DOI: https://doi.org/10.21468/SciPostPhys.8.5.072

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