SciPost Submission Page
Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
by Aleksey Cherman, Theodore Jacobson, Yuya Tanizaki, Mithat Ünsal
 Published as SciPost Phys. 8, 072 (2020)
Submission summary
As Contributors:  Theo Jacobson 
Arxiv Link:  https://arxiv.org/abs/1908.09858v3 (pdf) 
Date accepted:  20200402 
Date submitted:  20200313 01:00 
Submitted by:  Jacobson, Theo 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We show that $2$d adjoint QCD, an $SU(N)$ gauge theory with one massless adjoint Majorana fermion, has a variety of mixed 't Hooft anomalies. The anomalies are derived using a recent mod $2$ index theorem and its generalization that incorporates 't Hooft flux. Anomaly matching and dynamical considerations are used to determine the groundstate structure of the theory. The anomalies, which are present for most values of $N$, are matched by spontaneous chiral symmetry breaking. We find that massless $2$d adjoint QCD confines for $N >2$, except for test charges of $N$ality $N/2$, which are deconfined. In other words, $\mathbb Z_N$ center symmetry is unbroken for odd $N$ and spontaneously broken to $\mathbb Z_{N/2}$ for even $N$. All of these results are confirmed by explicit calculations on small $\mathbb{R}\times S^1$. We also show that this nonsupersymmetric theory exhibits exact BoseFermi degeneracies for all states, including the vacua, when $N$ is even. Furthermore, for most values of $N$, $2$d massive adjoint QCD describes a nontrivial symmetryprotected topological (SPT) phase of matter, including certain cases where the number of interacting Majorana fermions is a multiple of $8$. As a result, it fits into the classification of $(1+1)$d SPT phases of interacting Majorana fermions in an interesting way.
Ontology / Topics
See full Ontology or Topics database.Published as SciPost Phys. 8, 072 (2020)
Author comments upon resubmission
List of changes
Altered equation 1.1 to include perturbatively marginal fourFermi terms allowed by symmetries, and revised footnote 1 to reflect this change in presentation.
Corrected the proof given in footnote 3 that we have found all internal symmetries of the theory.
Revised the paragraphs at the end of page 6 regarding the fourFermi terms to address comments made by Referee 3.
Added footnote 13 to address questions raised by Referee 3 about the breaking of center symmetry to a subgroup.
Changed the wording in the second to last paragraph of section 6, taking into account the fourth comment by Referee 3.
Added a paragraph on page 39 clarifying which noncontractible line operator is deconfined on the cylinder with periodic boundary conditions.
Added two new paragraphs just before section 8.1 to emphasize why numerical lightcone studies in the literature did not observe BoseFermi degeneracy.
Changed the wording leading up to equation 8.2 to incorporate the suggestions of Referee 2.
Added figure 4 to illustrate the BoseFermi degeneracy of the massless theory on the cylinder.
Added a discussion at the top of page 46 about the vanishing of the chargeconjugationtwisted partition function at large N.
Reorganized section 8 to include a subsection focusing on BoseFermi degeneracy without supersymmetry. We removed the misleading example of a free Majorana fermion in two spacetime dimensions, and added arguments ruling out spontaneously broken SUSY or emergent SUSY at long distances.
Added a discussion in section 9 further commenting on the discrepancy between our results and numerical studies in the literature.
Changed the wording in the third bullet point in section 10.
Corrected typos generously pointed out by Referee 2.