Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory

TL;DR

This paper explores the Stokes phenomena in isomonodromy systems related to non-critical string/M-theory, revealing universal structures and connections to quantum integrable systems, extending the ODE/IM correspondence.

Contribution

It uncovers universal recursion equations for multi-cut boundary conditions and links Stokes multipliers to Hirota equations, broadening the understanding of quantum integrability in non-critical string theories.

Findings

Universal form of multi-cut boundary-condition recursion equations.

Explicit solutions for Stokes multipliers in wide classes of (k,r).

Connection between Stokes multipliers and quantum integrable systems via Hirota equations.

Abstract

We study Stokes phenomena of the k \times k isomonodromy systems with an arbitrary Poincar\'e index r, especially which correspond to the fractional-superstring (or parafermionic-string) multi-critical points (\hat p,\hat q)=(1,r-1) in the k-cut two-matrix models. Investigation of this system is important for the purpose of figuring out the non-critical version of M theory which was proposed to be the strong-coupling dual of fractional superstring theory as a two-matrix model with an infinite number of cuts. Surprisingly the multi-cut boundary-condition recursion equations have a universal form among the various multi-cut critical points, and this enables us to show explicit solutions of Stokes multipliers in quite wide classes of (k,r). Although these critical points almost break the intrinsic Z_k symmetry of the multi-cut two-matrix models, this feature makes manifest a connection between the multi-cut boundary-condition recursion equations and the structures of quantum integrable systems. In particular, it is uncovered that the Stokes multipliers satisfy multiple Hirota equations (i.e. multiple T-systems). Therefore our result provides a large extension of the ODE/IM correspondence to the general isomonodromy ODE systems endowed with the multi-cut boundary conditions. We also comment about a possibility that N=2 QFT of Cecotti-Vafa would be "topological series" in non-critical M theory equipped with a single quantum integrability.