A Hurwitz theory avatar of open-closed strings

TL;DR

This paper explores an infinite-dimensional Hurwitz theory model that captures open-closed string interactions using algebraic structures like permutations and bipartite graphs, revealing deep links between symmetric and linear group theories.

Contribution

It introduces a novel infinite-dimensional Hurwitz string model that unifies open and closed string sectors through algebraic structures, highlighting their interrelation.

Findings

Representation of open-closed strings via permutations and bipartite graphs

Existence of two distinct multiplications reflecting symmetric and linear group theories

Deep interrelation between symmetric and linear groups in the model

Abstract

We review and explain an infinite-dimensional counterpart of the Hurwitz theory realization of algebraic open-closed string model a la Moore and Lizaroiu, where the closed and open sectors are represented by conjugation classes of permutations and the pairs of permutations, i.e. by the algebra of Young diagrams and bipartite graphes respectively. An intriguing feature of this Hurwitz string model is coexistence of two different multiplications, reflecting the deep interrelation between the theory of symmetric and linear groups S_\infty and GL(\infty).