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Noninvertible Time-Reversal Symmetry
Yichul Choi1,2, Ho Tat Lam3, Shu-Heng Shao1
1C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, New York 11794, USA.
Physical Review Letters
|April 17, 2023
Summary
We discovered a new noninvertible time-reversal symmetry in gauge theories at rational angles θ=πp/N. This symmetry, unlike previously known ones, is implemented by a conserved operator and exists beyond θ=0 or π.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- Gauge Theory
Background:
- Time-reversal symmetry in gauge theory is typically considered to exist only at specific angles (θ=0 or π).
- Existing understanding limits the scope of time-reversal symmetry to these discrete points for a 2π-periodic θ angle.
Purpose of the Study:
- To investigate the existence of time-reversal symmetry beyond the commonly accepted conditions in gauge theories.
- To explore the nature and implementation of such symmetries in various theoretical models.
Main Methods:
- Analysis of free Maxwell theory and massive Quantum Electrodynamics (QED).
- Identification of conserved, antilinear operators implementing noninvertible symmetries.
- Extension of the analysis to non-Abelian gauge theories, including N=4 SU(2) super Yang-Mills theory.
Main Results:
- A noninvertible time-reversal symmetry exists at every rational θ angle (θ=πp/N) in free Maxwell theory and massive QED.
- This symmetry is realized by a conserved, antilinear operator that lacks an inverse.
- Similar noninvertible time-reversal symmetries were identified in non-Abelian gauge theories, specifically along |τ|=1 on the conformal manifold of N=4 SU(2) super Yang-Mills theory.
Conclusions:
- The conventional understanding of time-reversal symmetry in gauge theory needs revision.
- Noninvertible time-reversal symmetries offer a broader perspective on symmetry in quantum field theory.
- These findings open new avenues for exploring fundamental symmetries in theoretical physics.
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