ADE Little String Theory on a Riemann Surface (and Triality)

TL;DR

This paper explores ADE type (2,0) little string theories via IIB string compactification, deriving related 5d gauge theories and establishing a connection with q-deformed ADE Toda conformal blocks, generalizing the A_n triality.

Contribution

It introduces a new framework for ADE little string theories, deriving 5d quiver gauge theories, and generalizes the A_n triality to all ADE Lie algebras using IIB string theory.

Findings

Derived 5d ADE quiver gauge theories from little string compactification.

Established the equivalence between the partition function and q-deformed ADE Toda conformal blocks.

Generalized A_n triality to all ADE Lie algebras.

Abstract

We initiate the study of (2,0) little string theory of ADE type using its definition in terms of IIB string compactified on an ADE singularity. As one application, we derive a 5d ADE quiver gauge theory that describes the little string compactified on a sphere with three full punctures, at low energies. As a second application, we show the partition function of this theory equals the 3-point conformal block of ADE Toda CFT, q-deformed. To establish this, we generalize the A_n triality of \cite{AHS} to all ADE Lie algebras; IIB string perspective is crucial for this as well.