Boundary correlation numbers in one matrix model

Abstract

We introduce one matrix model coupled to multi-flavor vectors. The two-flavor vector model is demonstrated to reproduce the two-point correlation numbers of boundary primary fields of two dimensional (2, 2p+1) minimal Liouville gravity on disk, generalizing the loop operator (resolvent) description. The model can properly describe non-trivial boundary conditions for the matter Cardy state as well as for the Liouville field. From this we propose that the n-flavor vector model will be suited for producing the boundary correlation numbers with n different boundary conditions on disk.

16 pages, 3 figures, add elaboration on matter Cardy state and references

References in corpus (15)

• 2D Gravity and Random Matrices
• Lectures on 2D gravity and 2D string theory (TASI 1992)
• World Sheet and Space Time Physics in Two Dimensional (Super) String Theory
• Boundary Liouville Field Theory: Boundary Three Point Function
• Boundary structure constants for the A-series Virasoro minimal models
• Conformal boundary loop models
• On Correlation Numbers in 2D Minimal Gravity and Matrix Models
• Boundary Liouville Theory and 2D Quantum Gravity
• Boundary Correlators in 2D Quantum Gravity: Liouville versus Discrete Approach
• Minimal Open Strings
• Boundary operators in the O(n) and RSOS matrix models
• Perturbed Conformal Field Theory on Fluctuating Sphere
• Bulk one-point function on disk in one-matrix model
• Boundary transitions of the O(n) model on a dynamical lattice
• Flavour from partially resolved singularities

Cited by in corpus (18)

• Liouville quantum gravity -- holography, JT and matrices
• Degenerate operators in JT and Liouville (super)gravity
• Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory
• Boundary operators in minimal Liouville gravity and matrix models
• The Spectrum of FZZT Branes Beyond the Planar Limit
• Open KdV hierarchy and minimal gravity on disk
• Bulk-boundary correlators in the hermitian matrix model and minimal Liouville gravity
• FZZT Brane Relations in the Presence of Boundary Magnetic Fields
• Open minimal strings and open Gelfand-Dickey hierarchies
• Minimal gravity and Frobenius manifolds: bulk correlation on sphere and disk
• Boundary operators in the one-matrix model
• Dual Frobenius manifolds of minimal gravity on disk
• From minimal gravity to open intersection theory
• Open KdV hierarchy of 2d minimal gravity of Lee-Yang series
• The null identities for boundary operators in the $(2,2p+1)$ minimal gravity
• Wronskians, dualities and FZZT-Cardy branes
• Sums of Random Matrices and the Potts Model on Random Planar Maps
• Random Matrices, Boundaries and Branes