Abstract
We study the duality between JT gravity and the double-scaled matrix model including their respective deformations. For these deformed theories we relate the thermal partition function to the generating function of topological gravity correlators that are determined as solutions to the KdV hierarchy. We specialise to those deformations of JT gravity coupled to a gas of defects, which conforms with known results in the literature. We express the (asymptotic) thermal partition functions in a low temperature limit, in which non-perturbative corrections are suppressed and the thermal partition function becomes exact. In this limit we demonstrate that there is a Hawking-Page phase transition between connected and disconnected surfaces for this instance of JT gravity with a transition temperature affected by the presence of defects. Furthermore, the calculated spectral form factors show the qualitative behaviour expected for a Hawking-Page phase transition. The considered deformations cause the ramp to be shifted along the real time axis. Finally, we comment on recent results related to conical Weil-Petersson volumes and the analytic continuation to two-dimensional de Sitter space.
Highlights
The last term contains a Gibbons-Hawking-York boundary term together with a counterterm that ensures a finite result when removing the regularisation of the position of the AdS2 boundary
We study the duality between JT gravity and the double-scaled matrix model including their respective deformations
In this work we focus on the structure of deformations to JT gravity and the resulting modifications to the thermal partition functions appearing on the left hand side of the duality (1.3)
Summary
To set the stage and to introduce the used notation, we first collect some mathematical preliminaries on the Weil-Petersson volumes of hyperbolic Riemann surfaces with geodesic boundary components and conical singularities from the perspective of intersection theory on the moduli spaces of stable curves. The class κ1 is proportional to the Weil-Petersson Kähler form ωWP [47] Upon integrating such cohomology classes over Mg,n we obtain (rational) intersection numbers that are collected in correlators. As the first Miller-Morita-Mumford class κ1 is proportional to the Weil-Petersson Kähler form ωWP (cf eq (2.4)), the function G(2π2, {tk = 0}) evaluated at tk = 0 readily. The generating function for hyperbolic Riemann surfaces with boundary components of geodesic lengths b1, .
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