Abstract
In this paper, we completely characterize time-reversal-invariant three-dimensional Chern–Simons gauge theories with torus gauge group. At the level of the Lagrangian, toral Chern–Simons theory is defined by an integral lattice, while at the quantum level, it is entirely determined by a quadratic function on a finite Abelian group and an integer mod 24. We find that quantum time-reversally symmetric theories can be defined by classical Lagrangians defined by integral lattices which have self-perpendicular embeddings into a unimodular lattice. We find that the quantum toral Chern–Simons theory admits a time-reversal symmetry iff the higher Gauss sums of the associated modular tensor category are real. We conjecture that the reality of the higher Gauss sums is necessary and sufficient for a general non-Abelian Chern–Simons to admit quantum T-symmetry.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 673-714 |
| Number of pages | 42 |
| Journal | Annales Henri Poincare |
| Volume | 25 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2024 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics