Cap amplitudes in random matrix models

2025/09/04 by Okuyama, Kazumi
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2509.03930

Abstract

For general one-matrix models in the large N limit, we introduce the cap amplitude ψ(b) as the expansion coefficient of the 1-form ydx on the spectral curve. We find that the dilaton equation for the discrete volume N_g,n of the moduli space of genus-g Riemann surfaces with n boundaries is interpreted as gluing the cap amplitude along one of the boundaries. In this process, one of the boundaries is capped and the number of boundaries decreases by one. In a similar manner, the genus-g free energy F_g is obtained by gluing the cap amplitude to N_g,1.

Citations

• Sphere amplitudes and observing the universe's size
• de Sitter JT gravity from double-scaled SYK
• An entropic puzzle in periodic dilaton gravity and DSSYK
• Baby universe operators in the ETH matrix model of double-scaled SYK
• The dilaton gravity hologram of double-scaled SYK
• Discrete analogue of the Weil-Petersson volume in double scaled SYK
• Two dimensional Nearly de Sitter gravity
• JT gravity as a matrix integral
• Polynomials representing Eynard-Orantin invariants
• Algebraic methods in random matrices and enumerative geometry
• String and dilaton equations for counting lattice points in the moduli space of curves
• Invariants of algebraic curves and topological expansion
• Random Matrices

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• A review of the 1/N expansion in random tensor models
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• Conservation Laws of Random Matrix Theory