Compactified Little String Theories and Compact Moduli Spaces of Vacua

TL;DR

This paper explores how compactified little string theories have inherently compact moduli spaces of vacua, revealing connections to compact string geometries and describing the structure of Coulomb branches in various compactifications.

Contribution

It demonstrates that compactified little string theories possess compact moduli spaces of vacua that probe compact string geometries, providing explicit descriptions for different compactification scenarios.

Findings

Compactified little string theories have compact moduli spaces of vacua.

The Coulomb branch in 3d theories is given by spaces like T^4, K3, or instanton moduli spaces.

In 4d theories, the Coulomb branch forms a compact, elliptically-fibered space.

Abstract

It is emphasized that compactified little string theories have compact moduli spaces of vacua, which globally probe compact string geometry. Compactifying various little string theories on T^3 leads to 3d theories with exact, quantum Coulomb branch given by: an arbitrary T^4 of volume M_s^2, an arbitrary K3 of volume M_s^2, and moduli spaces of G=SU(N), SO(2N), or E_{6,7,8} instantons on an arbitrary T^4 or K3 of fixed volume. Compactifying instead on a T^2 leads to 4d theories with a compact Coulomb branch base which, when combined with the exact photon gauge coupling fiber, is a compact, elliptically-fibered space related to the above spaces.