Title: Time-reversal symmetry, anomalies, and dualities in (2+1)$$d$$

Abstract

We study continuum quantum field theories in 2+1 dimensions with time-reversal symmetry \cal T . The standard relation {\cal T}^2=(-1)^F is satisfied on all the “perturbative operators” i.e. polynomials in the fundamental fields and their derivatives. However, we find that it is often the case that acting on more complicated operators {\cal T}^2=(-1)^F {\cal M} with \cal M a non-trivial global symmetry. For example, acting on monopole operators, \cal M could be \pm1 $\pm 1$ depending on the magnetic charge. We study in detail U(1) $U\left(1\right)$ gauge theories with fermions of various charges. Such a modification of the time-reversal algebra happens when the number of odd charge fermions is 2 ~{\rm mod }~4 , e.g. in QED with two fermions. Our work also clarifies the dynamics of QED with fermions of higher charges. In particular, we argue that the long-distance behavior of QED with a single fermion of charge 2 $2$ is a free theory consisting of a Dirac fermion and a decoupled topological quantum field theory. The extension to an arbitrary even charge is straightforward. The generalization of these abelian theories to SO(N) $SO\left(N\right)$ gauge theories with fermions in the vector or in two-index tensor representations leads to new results and new consistency conditions on previously suggested scenarios for the dynamics of these theories. Among these new results is a surprising non-abelian symmetry involving time-reversal.

Authors:

Cordova, Clay ^[1]; Hsin, Po-Shen ^[2]; Seiberg, Nathan ^[1]

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+ Show Author Affiliations

1. Institute for Advanced Study, Princeton University
2. Princeton University

Publication Date:

Fri Jul 20 00:00:00 EDT 2018

Sponsoring Org.:

USDOE

OSTI Identifier:

1461012

Grant/Contract Number:  

SC0009988

Resource Type:

Published Article

Journal Name:

SciPost Physics

Additional Journal Information:

Journal Name: SciPost Physics Journal Volume: 5 Journal Issue: 1; Journal ID: ISSN 2542-4653

Publisher:

Stichting SciPost

Country of Publication:

Netherlands

Language:

English