Periodic Schur Process, Cylindric Partitions and N=2* Theory

TL;DR

This paper explores the connection between refined topological string partition functions in string theory and combinatorial structures like the periodic Schur process and cylindric partitions, revealing dualities and quantization conditions.

Contribution

It demonstrates that certain string theory partition functions are examples of the periodic Schur process and relate to cylindric partitions, highlighting dualities and quantization effects.

Findings

Partition functions are examples of the periodic Schur process.

Partition functions relate to cylindric partitions with quantized parameters.

Level-rank duality manifests as exchange symmetry of Kahler parameters.

Abstract

Type IIA string theory compactified on an elliptic CY3-fold gives rise to N=2 U(1) gauge theory with an adjoint hypermultiplet. We study the refined open and closed topological string partition functions of this geometry using the refined topological vertex. We show that these partition functions, open and closed, are examples of periodic Schur process and are related to the generating function of the cylindric partitions if the Kahler parameters are quantized in units of string coupling. The level-rank duality appears as the exchange symmetry of the two Kahler parameters of the elliptic CY3-fold.