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

Abstract

We study Stokes phenomena of the k \times k isomonodromy systems with an arbitrary Poincaré 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.

43 pages, 3 figures; v2:references and comments added (footnote 24)

References in corpus (19)

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• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
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• Asymptotics of the instantons of Painleve I
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• Nonperturbative Effect in c=1 Noncritical String Theory and Penner Model
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• Fractional-Superstring Amplitudes, Multi-Cut Matrix Models and Non-Critical M Theory
• Bulk-boundary correlators in the hermitian matrix model and minimal Liouville gravity
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