Discrete theta angle from an O5-plane

TL;DR

This paper investigates 5d $Sp(1)$ gauge theories with an O5-plane, revealing how discrete theta angles influence global symmetry and phase structure through Seiberg-Witten curves and brane configurations.

Contribution

It introduces a method to compute Seiberg-Witten curves for theories with different theta angles from brane webs with O5-planes, highlighting their distinct strong coupling behaviors.

Findings

Different Seiberg-Witten curves for $ heta=0$ and $ heta=\pi$ theories.

Distinct phase structures in Coulomb branch at strong coupling.

Different $(p,q)$ 5-brane configurations with O5-plane.

Abstract

We consider 5d $\mathcal{N}=1$ $Sp(1)$ gauge theory based on a brane configuration with an O5-plane. At the UV fixed point, the theory with no matter enjoys enhanced global symmetry $SU(2)$ or $U(1)$ depending on the discrete theta angle $\theta=0, \pi$ (mod $2\pi$). A naive brane configuration with an O5-plane, however, does not distinguish two different theories, as it describes the weak coupling region. We devise a technique for computing 5d Seiberg-Witten curve of the two theories from the brane web with an O5-plane. Their Seiberg-Witten curves show that their M5 configurations under the presence of OM5-planes are different. The decompactification limit of each Seiberg-Witten curve also shows distinct phase structures in their Coulomb branch leading to significantly different $(p,q)$ 5-brane configurations with an O5-plane in the strong coupling region.