Instanton-Monopole Correspondence from M-Branes on $\mathbb{S}^1$ and Little String Theory

TL;DR

This paper explores the duality between instanton and monopole configurations in M-brane setups and little string theories, revealing a new correspondence and T-duality manifestations through detailed BPS state analysis.

Contribution

It introduces a novel instanton-monopole correspondence in M-brane configurations and connects BPS counting functions across dual gauge theories and string theories.

Findings

BPS counting functions can be expressed as linear combinations of M5-M2-brane configurations.

Free energies in dual theories match for certain M2-brane setups.

The results demonstrate a new instanton-monopole correspondence and T-duality in little string theories.

Abstract

We study BPS excitations in M5-M2-brane configurations with a compact transverse direction, which are also relevant for type IIa and IIb little string theories. These configurations are dual to a class of toric elliptically fibered Calabi-Yau manifolds $X_N$ with manifest $SL(2, \mathbb{Z}) \times SL(2,\mathbb{Z})$ modular symmetry. They admit two dual gauge theory descriptions. For both, the non-perturbative partition function can be written as an expansion of the topological string partition function of $X_N$ with respect to either of the two modular parameters. We analyze the resulting BPS counting functions in detail and find that they can be fully constructed as linear combinations of the BPS counting functions of M5-M2-brane configurations with non-compact transverse directions. For certain M2-brane configurations, we also find that the free energies in the two dual theories agree with each other, which points to a new correspondence between instanton and monopole configurations. These results are also a manifestation of T-duality between type IIa and IIb little string theories.