F-theory and the Classification of Little Strings

TL;DR

This paper systematically classifies little string theories (LSTs) using F-theory geometry, revealing their relation to 6D superconformal field theories and demonstrating T-duality via elliptic fibration exchanges.

Contribution

It provides a geometric construction of all LSTs with multiple tensors by extending 6D SCFTs and shows their embedding within SCFTs, advancing the understanding of their structure.

Findings

All LSTs with multiple tensors are extensions of 6D SCFTs.

All 6D SCFTs embed naturally into LSTs.

Exchanging elliptic fibrations corresponds to T-duality in 6D theories.

Abstract

Little string theories (LSTs) are UV complete non-local 6D theories decoupled from gravity in which there is an intrinsic string scale. In this paper we present a systematic approach to the construction of supersymmetric LSTs via the geometric phases of F-theory. Our central result is that all LSTs with more than one tensor multiplet are obtained by a mild extension of 6D superconformal field theories (SCFTs) in which the theory is supplemented by an additional, non-dynamical tensor multiplet, analogous to adding an affine node to an ADE quiver, resulting in a negative semidefinite Dirac pairing. We also show that all 6D SCFTs naturally embed in an LST. Motivated by physical considerations, we show that in geometries where we can verify the presence of two elliptic fibrations, exchanging the roles of these fibrations amounts to T-duality in the 6D theory compactified on a circle.