Noninvertible Time-Reversal Symmetry - INSPIRE

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Noninvertible Time-Reversal Symmetry

Yichul Choi
(
- YITP, Stony Brook and
- Stony Brook U., New York, SCGP
)
,
Ho Tat Lam
(
- MIT, Cambridge, CTP
)
,
Shu-Heng Shao
(
- YITP, Stony Brook
)

Aug 8, 2022

31 pages

Published in:

Phys.Rev.Lett. 130 (2023) 13, 131602

Published: Mar 28, 2023

e-Print:

2208.04331 [hep-th]

DOI:

10.1103/PhysRevLett.130.131602 (publication)

Report number:

YITP-SB-2022-28,
MIT-CTP/5457

View in:

ADS Abstract Service

reference search106 citations

Citations per year

Abstract: (APS)

In gauge theory, it is commonly stated that time-reversal symmetry only exists at

θ = 0

or

π

for a

2 π

-periodic

θ

angle. In this Letter, we point out that in both the free Maxwell theory and massive QED, there is a noninvertible time-reversal symmetry at every rational

θ

angle, i.e.,

θ = π p / N

. The noninvertible time-reversal symmetry is implemented by a conserved, antilinear operator without an inverse. It is a composition of the naive time-reversal transformation and a fractional quantum Hall state. We also find similar noninvertible time-reversal symmetries in non-Abelian gauge theories, including the

N = 4

SU(2) super Yang-Mills theory along the locus

| τ | = 1

on the conformal manifold.

Note:

31 pages

time reversal: symmetry
space: conformal
gauge field theory: Yang-Mills
quantum electrodynamics: massive
gauge field theory: nonabelian
supersymmetry
fractional
pi p
SU(2)
conservation law

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