Combinatorics of Solitons in Noncritical String Theory

TL;DR

This paper explores the combinatorial structure of solitons in low-dimensional string theory, demonstrating that their weights are uniquely determined by integrability constraints related to the KP hierarchy and $W_{1+ abla}$ symmetry.

Contribution

It establishes a link between soliton combinatorics and integrable hierarchies, providing a novel method to determine soliton weights in noncritical string theory.

Findings

Weights are uniquely determined by KP $ au$ function conditions.

Partition functions with soliton backgrounds satisfy integrability constraints.

The approach connects soliton combinatorics with integrable systems theory.

Abstract

We study the combinatorics of solitons in $D<2$ (or $c<1$) string theory. The weights in the summation over multi-solitons are shown to be automatically determined if we further require that the partition function with soliton background be a $\tau$ function of the KP hierarchy, in addition to the $W_{1+\infty}$ constraint.