SL$(2,\mathbb{Z})$ action on quantum field theories with U(1) subsystem symmetry

TL;DR

This paper explores the SL(2,Z) symmetry transformations in five-dimensional quantum field theories with U(1) subsystem symmetry, revealing triviality of certain exotic theories and defining the S and T operations within this framework.

Contribution

It extends the SL(2,Z) action to 5D U(1) subsystem symmetric theories, clarifying the triviality of exotic theories and constructing the group operations.

Findings

Exotic level 1 BF and Chern-Simons theories are trivial or almost trivial.

SL(2,Z) group operations are well-defined up to a phase in the studied spacetime.

SL(2,Z) action is demonstrated explicitly on the φ theory.

Abstract

We consider SL$(2,\mathbb{Z})$ action on quantum field theories with U(1) subsystem symmetry in five dimensions. This is an analog of the SL$(2,\mathbb{Z})$ action considered in arXiv:hep-th/0307041. We show that the exotic level 1 BF theory and the exotic level 1 Chern-Simons theories are trivial and almost trivial, respectively. By using this fact, we define S operation and T operation. These operations make SL$(2,\mathbb{Z})$ group up to a possible invertible phase that is unity within the space-times treated in this paper. We also demonstrate SL$(2,\mathbb{Z})$ action on the $\varphi$ theory as an example.