Boundary operators in minimal Liouville gravity and matrix models

Abstract

We interpret the matrix boundaries of the one matrix model (1MM) recently constructed by two of the authors as an outcome of a relation among FZZT branes. In the double scaling limit, the 1MM is described by the (2,2p+1) minimal Liouville gravity. These matrix operators are shown to create a boundary with matter boundary conditions given by the Cardy states. We also demonstrate a recursion relation among the matrix disc correlator with two different boundaries. This construction is then extended to the two matrix model and the disc correlator with two boundaries is compared with the Liouville boundary two point functions. In addition, the realization within the matrix model of several symmetries among FZZT branes is discussed.

26 pages

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Cited by in corpus (10)

• 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
• The Spectrum of FZZT Branes Beyond the Planar Limit
• Bulk-boundary correlators in the hermitian matrix model and minimal Liouville gravity
• FZZT Brane Relations in the Presence of Boundary Magnetic Fields
• The null identities for boundary operators in the $(2,2p+1)$ minimal gravity
• Random Matrices, Boundaries and Branes
• Wronskians, dualities and FZZT-Cardy branes
• Sums of Random Matrices and the Potts Model on Random Planar Maps