Cap Amplitudes in Random Matrix Models
Abstract
Abstract For general one-matrix models in the large-N limit, we introduce the cap amplitude $\psi (b)$ 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 $N_{g,1}$.
Fields of Study & Subjects
Random Matrices and Applications
Black Holes and Theoretical Physics
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Progress of Theoretical and Experimental Physics
- Volume
- 2026
- Issue
- 3
- Publication date
- 10 February 2026
- Language
- EN