FZZT branes in JT gravity and topological gravity

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.

Low-temperature entropy in JT gravity

For ensembles of Hamiltonians that fall under the Dyson classification of random matrices with β ∈ {1, 2, 4}, the low-temperature mean entropy can be shown to vanish as 〈S(T)〉 ∼ κTβ + 1. A similar relation holds for Altland-Zirnbauer ensembles. JT gravity has been shown to be dual to the double-scaling limit of a β = 2 ensemble, with a classical eigenvalue density $$ \propto {e}^{S_0}\sqrt{E} $$ ∝ e S 0 E when 0 < E ≪ 1. We use universal results about the distribution of the smallest eigenvalues in such ensembles to calculate κ up to corrections that we argue are doubly exponentially small in S0.