On 6d "Gauge" Theories with Irrational Theta Angle

TL;DR

This paper explores 6d gauge theories with irrational theta angles, proposing a framework from string theory constructions that suggests a generalized limit for arbitrary theta, despite the non-free nature of the 10d theory.

Contribution

It introduces a new perspective on 6d gauge theories with irrational theta angles using (p,q) 5-branes and proposes a generalized limit for arbitrary theta angles.

Findings

Theories constructed from (p,q) 5-branes have rational theta angles.

A new limit potentially defines a decoupled 6d theory for arbitrary theta.

The 10d theta angle relates to the 6d theta angle via brane configurations.

Abstract

A recent proposal for 6d "gauge" theories with rational theta angle is discussed. These theories were constructed from n_C coinciding (p,q) 5-branes of IIB in the limit of vanishing string constant. They have (1,1) supersymmetry and the low energy theory is 6d Yang-Mills with gauge group SU(n_C) and a rational theta angle theta_6/(2 pi)=f/q, where fp=1 (mod q). By changing the point of view, considering the (p,q) 5-branes to be D5-branes, the 6d theta angle is identified with a 10d theta angle. This point of view together with some assumptions suggests a generalization of the previous limit to arbitrary theta. This limit seems to define a decoupled 6d theory even though the 10d theory does not become free in general.