Superloop Equations and Two Dimensional Supergravity

Abstract

We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of $(2,4m)$-minimal superconformal models coupled to $2D$-supergravity. The basic assumption in our presentation is a set of super-Virasoro constraints imposed on the partition function. We recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also able to evaluate all planar loop correlation functions in the continuum limit. We find evidence to identify the integrable hierarchy of non-linear equations describing the double scaling limit as a supersymmetric generalization of KP studied by Rabin.

34 pages

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• Supereigenvalue Model and Dijkgraaf-Vafa Proposal
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• Fermionic flows and tau function of the N=(1|1) superconformal Toda lattice hierarchy
• Super-quantum curves from super-eigenvalue models
• The Supereigenvalue Model in the Double-Scaling Limit
• Super Quantum Airy Structures
• Iterative Solution of the Supereigenvalue Model
• From CFT to Ramond super-quantum curves
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Riemann-Liouville integrals of fractional order and extended KP hierarchy
• Non-critical strings at high energy
• The sTB-B Hierarchy
• Macroscopic $n$-Loop Amplitude for Minimal Models Coupled to Two-Dimensional Gravity: Fusion Rules and Interactions
• Macroscopoic Three-Loop Amplitudes and the Fusion Rules from the Two-Matrix Model
• Supereigenvalue Models and Topological Recursion
• Correlators in the supereigenvalue model in the Ramond sector
• Topological Recursion in The Ramond Sector
• Symmetries of Supersymmetric Integrable Hierarchies of KP Type
• String Geometry and Non-perturbative Formulation of String Theory
• Continuum Annulus Amplitude from the Two-Matrix Model
• On the amplitudes for non-critical n=2 supuerstrings
• The Chiral Supereigenvalue Model
• Non-critical superstrings: a comparison between continuum and discrete approaches
• Macdonald polynomials for super-partitions
• Supermatrix models and multi ZZ-brane partition functions in minimal superstring theories
• Canonical gauge equivalences of the sAKNS and sTB hierarchies
• Correlators in the Gaussian and chiral supereigenvalue models in the Neveu-Schwarz sector
• Correlators in non-critical superstrings including the spinor emission vertex
• $\mathcal{N}=1$ Super Topological Recursion
• Higher spin constraints and the super $(W_{\frac{\infty }{2}}\oplus W_{\frac{1+\infty }{2}})$ algebra in the super eigenvalue model
• Non-linear Structures in Non-critical NSR String
• Loop equations for generalised eigenvalue models
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• World-Sheets from N=4 Super Yang-Mills
• Susy Hierarchies and Affine Algebras