FZZT branes in JT gravity and topological gravity

TL;DR

This paper explores FZZT branes within topological and JT gravity, revealing their effects on matrix models, boundary conditions, and spectral properties, including non-perturbative formulations and eigenvalue behavior.

Contribution

It provides a detailed analysis of FZZT branes in topological gravity, including their perturbative and non-perturbative effects, and connects these to matrix models and spectral phenomena in JT gravity.

Findings

FZZT branes correspond to determinant insertions in matrix models.

Adding FZZT branes shifts couplings and affects Weil-Petersson volumes.

Eigenvalue density exhibits a void and oscillations due to FZZT branes.

Abstract

We study Fateev-Zamolodchikov-Zamolodchikov-Teschner (FZZT) branes in Witten-Kontsevich topological gravity, which includes Jackiw-Teitelboim (JT) gravity as a special case. Adding FZZT branes to topological gravity corresponds to inserting determinant operators in the dual matrix integral and amounts to a certain shift of the infinitely many couplings of topological gravity. We clarify the perturbative interpretation of adding FZZT branes in the genus expansion of topological gravity in terms of a simple boundary factor and the generalized Weil-Petersson volumes. As a concrete illustration we study JT gravity in the presence of FZZT branes and discuss its relation to the deformations of the dilaton potential that give rise to conical defects. We then construct a non-perturbative formulation of FZZT branes and derive a closed expression for the general correlation function of multiple FZZT branes and multiple macroscopic loops. As an application we study the FZZT-macroscopic loop correlators in the Airy case. We observe numerically a void in the eigenvalue density due to the eigenvalue repulsion induced by FZZT-branes and also the oscillatory behavior of the spectral form factor which is expected from the picture of eigenbranes.