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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.