Fractional-Superstring Amplitudes, Multi-Cut Matrix Models and Non-Critical M Theory

Abstract

Multi-cut two-matrix models are studied in the Z_k symmetry breaking k-cut (\hat p,\hat q) critical points which should correspond to (\hat p,\hat q) minimal k-fractional superstring theory. FZZT-brane or macroscopic loop amplitudes are obtained in all of these critical points and found to have two kinds of solutions in general. Each of these solutions is expressed by hyperbolic cosine or sine functions with proper phase shifts. The algebraic geometries and ZZ-brane disk amplitudes (instanton actions) of these solutions are also studied. In particular, our results suggest that minimal \infty-fractional superstring theory can be viewed as a mother theory which includes all the minimal k-fractional superstring theories (k=1,2,...) as its perturbative vacua in the weak-coupling string landscape. Our results also indicate that, in the strong coupling regime of this fractional superstring theory, there is a three-dimensional theory which would be understood as the non-critical version of M theory in the sense proposed by P. Horava and C. A. Keeler.

47 pages, 6 figures; references added v2

References in corpus (5)

• Notes on the algebraic curves in (p,q) minimal string theory
• Geometrical interpretation of the topological recursion, and integrable string theories
• Fractional supersymmetric Liouville theory and the multi-cut matrix models
• Macroscopic loop amplitudes in the multi-cut two-matrix models
• Notes on D-branes and dualities in (p,q) minimal superstring theory

Cited by in corpus (6)

• Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory
• Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models
• Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory
• Analytic Study for the String Theory Landscapes via Matrix Models
• Duality Constraints on String Theory: Instantons and spectral networks
• Wronskians, dualities and FZZT-Cardy branes