Brane Webs and Random Processes

TL;DR

This paper explores the connection between brane web configurations in string theory and combinatorial processes like cylindric Schur processes and plane partitions, generalizing previous results to cases with period N.

Contribution

It introduces a novel link between $(p,q)$ 5-brane webs and cylindric Schur processes with arbitrary period N, extending prior work limited to period 1.

Findings

Partition functions of brane webs relate to cylindric Schur processes with period N.

Open string amplitudes are described by generating functions of cylindric plane partitions.

Generalization from period 1 to arbitrary period N in brane web configurations.

Abstract

We study $(p,q)$ 5-brane webs dual to certain $N$ M5-brane configurations and show that the partition function of these brane webs gives rise to cylindric Schur process with period $N$. This generalizes the previously studied case of period $1$. We also show that open string amplitudes corresponding to these brane webs are captured by the generating function of cylindric plane partitions with profile determined by the boundary conditions imposed on the open string amplitudes.