A Twist on Heterotic Little String Duality

TL;DR

This paper expands the web of T-dualities among heterotic NS5-brane theories with twists involving automorphisms, establishing dualities via M-theory compactifications and constructing new 5D theories.

Contribution

It introduces new twisted heterotic theories with automorphism twists, and develops invariants to establish dualities and construct novel 5D theories.

Findings

Established dualities between twisted and untwisted theories.

Constructed new 5D theories, including a CHL-like twisted theory.

Proved dualities using M/F-theory compactifications and geometric analysis.

Abstract

In this work, we significantly expand the web of T-dualities among heterotic NS5-brane theories with eight supercharges. This is achieved by introducing twists involving outer automorphisms of discrete gauge/flavor factors and tensor multiplet permutations along the compactification circle. We assemble field theory data that we propose as invariants across T-dual theories, comprised of twisted Coulomb branch dimensions, higher group structures and flavor symmetry ranks. Using this data, we establish a detailed field theory correspondence between singularities of the compactification space, the number five-branes in the theory, and the flavor symmetry factors. The twisted theories are realized via M-theory compactifications on non-compact genus-one fibered Calabi-Yau threefolds without section. This approach allows us to prove duality of twisted and (un-)twisted theories by leveraging M/F-theory duality and identifying inequivalent torus fibrations in the same geometry. We construct several new 5D theories, including a novel type of CHL-like twisted theory where the two M9 branes are identified. Using their field theory invariants, we also construct their dual theories.