Little Strings, Quasi-topological Sigma Model on Loop Group, and Toroidal Lie Algebras

TL;DR

This paper explores the connection between little string theory, loop group sigma models, and toroidal Lie algebras, revealing how ground and excited states form modules over these algebraic structures.

Contribution

It establishes a novel link between little string theory states and modules over affine and toroidal Lie algebras via a supersymmetric sigma model on CP^1.

Findings

Ground states form modules over affine Lie algebra.

Excited states form modules over toroidal Lie algebra.

Application to BPS sectors of M5-brane theory.

Abstract

We study the ground states and left-excited states of the A_{k-1} N=(2,0) little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP^1 with target space the based loop group of SU(k). The ground states, described by L^2-cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.