TY - JOUR
T1 - Noninvertible Time-Reversal Symmetry
AU - Choi, Yichul
AU - Lam, Ho Tat
AU - Shao, Shu Heng
N1 - Publisher Copyright: © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.
PY - 2023/3/31
Y1 - 2023/3/31
N2 - In gauge theory, it is commonly stated that time-reversal symmetry only exists at θ=0 or π for a 2π-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=πp/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.
AB - In gauge theory, it is commonly stated that time-reversal symmetry only exists at θ=0 or π for a 2π-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=πp/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.
UR - https://www.scopus.com/pages/publications/85152115347
U2 - 10.1103/PhysRevLett.130.131602
DO - 10.1103/PhysRevLett.130.131602
M3 - Article
C2 - 37067311
SN - 0031-9007
VL - 130
JO - Physical Review Letters
JF - Physical Review Letters
IS - 13
M1 - 131602
ER -