Spin(7) Orientifolds and 2d $\mathcal{N}= (0,1)$ Triality

TL;DR

This paper offers a geometric perspective on 2d $ =(0,1)$ gauge theory triality via Spin(7) orientifolds, revealing a richer structure that includes interpolations between $ =(0,2)$ and $ =(0,1)$ sectors.

Contribution

It introduces a geometric framework using Spin(7) orientifolds to understand and extend 2d $ =(0,1)$ triality, uncovering new possibilities beyond the original formulation.

Findings

Triality corresponds to multiple gauge theories from the same orientifold.

Universal involution in Spin(7) orientifolds reproduces original triality.

Extended triality includes theories with coupled $ =(0,2)$ and $ =(0,1)$ sectors.

Abstract

We present a new, geometric perspective on the recently proposed triality of 2d $\mathcal{N}=(0,1)$ gauge theories, based on its engineering in terms of D1-branes probing Spin(7) orientifolds. In this context, triality translates into the fact that multiple gauge theories correspond to the same underlying orientifold. We show how Spin(7) orientifolds based on a particular involution, which we call the universal involution, give rise to precisely the original version of $\mathcal{N}=(0,1)$ triality. Interestingly, our work also shows that the space of possibilities is significantly richer. Indeed, general Spin(7) orientifolds extend triality to theories that can be regarded as consisting of coupled $\mathcal{N}=(0,2)$ and $(0,1)$ sectors. The geometric construction of 2d gauge theories in terms of D1-branes at singularities therefore leads to extensions of triality that interpolate between the pure $\mathcal{N}=(0,2)$ and $(0,1)$ cases.