Little String Theory and Heterotic/Type II Duality

TL;DR

This paper explores the topological version of Little String Theory (LST), demonstrating how it can be used to compute low-energy effective terms and establishing dualities with heterotic strings, revealing structural consistencies.

Contribution

It introduces a topological string approach to LST, enabling efficient calculation of F^4 terms and clarifies dualities with heterotic strings near enhanced gauge symmetry points.

Findings

Topological string methods effectively compute F^4 terms in LST.

F^4 terms in heterotic string and LST match structurally.

Clarified roles of normalizable modes and operator identifications in holographic backgrounds.

Abstract

Little String Theory (LST) is a still somewhat mysterious theory that describes the dynamics near a certain class of time-like singularities in string theory. In this paper we discuss the topological version of LST, which describes topological strings near these singularities. For 5+1 dimensional LSTs with sixteen supercharges, the topological version may be described holographically in terms of the N=4 topological string (or the N=2 string) on the transverse part of the near-horizon geometry of NS5-branes. We show that this topological string can be used to efficiently compute the half-BPS F^4 terms in the low-energy effective action of the LST. Using the strong-weak coupling string duality relating type IIA strings on K3 and heterotic strings on T^4, the same terms may also be computed in the heterotic string near a point of enhanced gauge symmetry. We study the F^4 terms in the heterotic string and in the LST, and show that they have the same structure, and that they agree in the cases for which we compute both of them. We also clarify some additional issues, such as the definition and role of normalizable modes in holographic linear dilaton backgrounds, the precise identifications of vertex operators in these backgrounds with states and operators in the supersymmetric Yang-Mills theory that arises in the low energy limit of LST, and the normalization of two-point functions.