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We study open topological gravity in two dimensions, or, the intersection theory on the moduli space of open Riemann surfaces initiated by Pandharipande, Solomon and Tessler. The open free energy, the generating function for the open intersection numbers, obeys the open KdV equations and Buryaks differential equation and is related by a formal Fourier transformation to the Baker-Akhiezer wave function of the KdV hierarchy. Using these properties we study the genus expansion of the free energy in detail. We construct explicitly the genus zero part of the free energy. We then formulate a method of computing higher genus corrections by solving Buryaks equation and obtain them up to high order. This method is much more efficient than our previous approach based on the saddle point calculation. Along the way we show that the higher genus corrections are polynomials in variables that are expressed in terms of genus zero quantities only, generalizing the constitutive relation of closed topological gravity.
We study multi-boundary correlators of Witten-Kontsevich topological gravity in two dimensions. We present a method of computing an open string like expansion, which we call the t Hooft expansion, of the $n$-boundary correlator for any $n$ up to any
We define and study a holographic dual to the topological twist of $mathcal{N}=4$ gauge theories on Riemannian three-manifolds. The gravity duals are solutions to four-dimensional $mathcal{N}=4$ gauged supergravity, where the three-manifold arises as
Torsion gravity is a natural extension to Einstein gravity in the presence of the fermion matter sources. In this paper we adopt Walds covariant method of Noether charge to construct the quasi-local energy of the Einstein-Cartan-fermion system, and f
The quenched free energy, $F_Q(T){=}{-}Tlangle ln Z(T)rangle$, of various JT gravity and supergravity theories is explored, taking into account the key non-perturbative physics that is accessible using their matrix model formulations. The leading low
We quantize the two-dimensional projectable Horava-Lifshitz gravity with a bi-local as well as space-like wormhole interaction. The resulting quantum Hamiltonian coincides with the one obtained through summing over all genus in the string field theor