Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings

TL;DR

This paper derives exact instanton expansions for certain superconformal Chern-Simons theories using topological string theory, revealing universal structures and unexpected relations between different theories.

Contribution

It extends the known duality between ABJM matrix model and topological strings to new superconformal theories, identifying their instanton expansions and topological invariants.

Findings

Partition functions expressed via refined topological string free energy.

Different theories share similar universal functions with distinct invariants.

An unexpected relation between two superconformal Chern-Simons theories.

Abstract

It was known that the ABJM matrix model is dual to the topological string theory on a Calabi-Yau manifold. Using this relation it was possible to write down the exact instanton expansion of the partition function of the ABJM matrix model. The expression consists of a universal function constructed from the free energy of the refined topological string theory with an overall topological invariant characterizing the Calabi-Yau manifold. In this paper we explore two other superconformal Chern-Simons theories of the circular quiver type. We find that the partition function of one theory enjoys the same expression from the refined topological string theory as the ABJM matrix model with different topological invariants while that of the other is more general. We also observe an unexpected relation between these two theories.