Revisiting the second order formalism of JT gravity

We revisit the gravity path integral formalism of JT gravity. We explain how to gauge fix the path integral in the presence of asymptotic boundaries and conical defects, and resolve an ambiguity regarding the dilaton gravity operator that creates a conical defect. Along the way we study JT gravity coupled to matter on surfaces with defects of special opening angles, obtaining expressions for partition and two-point functions of matter fields. The two point function involves a summation over all geodesics on the surface, including self-intersecting geodesics, which we formally manage to include.Comment: 37 page

Quantum Maximin Surfaces

We formulate a quantum generalization of maximin surfaces and show that a quantum maximin surface is identical to the minimal quantum extremal surface, introduced in the EW prescription. We discuss various subtleties and complications associated to a maximinimization of the bulk von Neumann entropy due to corners and unboundedness and present arguments that nonetheless a maximinimization of the UV-finite generalized entropy should be well-defined. We give the first general proof that the EW prescription satisfies entanglement wedge nesting and the strong subadditivity inequality. In addition, we apply the quantum maximin technology to prove that recently proposed generalizations of the EW prescription to nonholographic subsystems (including the so-called "quantum extremal islands") also satisfy entanglement wedge nesting and strong subadditivity. Our results hold in the regime where backreaction of bulk quantum fields can be treated perturbatively in $G_{N}\hbar$, but we emphasize that they are valid even when gradients of the bulk entropy are of the same order as variations in the area, a regime recently investigated in new models of black hole evaporation in AdS/CFT.Comment: 52 pages, 9 figures, v2: updated text, v3: fixed typo

The Lion, the Witch, and the Wormhole: Ensemble averaging the symmetric product orbifold

We consider the ensemble average of two dimensional symmetric product orbifold CFTs $\text{Sym}^N(\mathbb{T}^D)$ over the Narain moduli space. We argue for a bulk dual given by $N$ copies of an abelian Chern-Simons theory coupled to topological gravity, endowed with a discrete gauge symmetry exchanging the $N$ copies. As a check of this proposal, we calculate the ensemble average of various partition and correlation functions of the symmetric product orbifold theory and compare the resulting expressions to gauge theory quantities in the bulk. We comment on the ensemble average of the tensionless string partition function on $\text{AdS}_3 \times \text{S}^3 \times \mathbb T^4$ by considering the specific case of $D=4$ with the addition of supersymmetry.Comment: 84 pages, 25 figure

Aspects of Low Dimensional Quantum Gravity

This thesis will be an exploration of various topics within low dimensional quantum gravity,with an emphasis on the gravitational path integral. We begin by studying two-dimensional Jackiw-Teitelboim (JT) gravity deformed by a gas of conical defects and we solve the model non-perturbatively. We then consider the problem of defining the Lorentzian gravity path integral through a contour rotation of the Euclidean path integral within the context of JT gravity. We demonstrate the agreement of integration domains and calculate the measure for the Lorentzian path integral. We then analyze ensemble averaging a family of two dimensional Conformal Field Theories and find a relation with an exotic three-dimensional bulk Chern-Simons theory