Reading between the lines of four-dimensional gauge theories

TL;DR

This paper explores how different choices of line operators in four-dimensional gauge theories lead to distinct but related physical theories, providing new insights into their dualities and phase structures.

Contribution

It clarifies the role of line operator choices and discrete parameters in the dynamics and dualities of 4D gauge theories, including supersymmetric cases.

Findings

Different line operator choices correspond to distinct physical theories.

Shifts in theta-angle permute these theories in some cases.

Discrete theta-like parameters label new classes of theories.

Abstract

Starting with a choice of a gauge group in four dimensions, there is often freedom in the choice of magnetic and dyonic line operators. Different consistent choices of these operators correspond to distinct physical theories, with the same correlation functions of local operators in R^4. In some cases these choices are permuted by shifting the theta-angle by 2pi. In other cases they are labeled by new discrete theta-like parameters. Using this understanding we gain new insight into the dynamics of four-dimensional gauge theories and their phases. The existence of these distinct theories clarifies a number of issues in electric/magnetic dualities of supersymmetric gauge theories, both for the conformal N=4 theories and for the low-energy dualities of N=1 theories.