Aspects of Wormholes in Quantum Gravity

Abstract

In this Dissertation, we study various implications of wormholes in quantum gravity. In Chapter 2, we start by discussing the implication of wormhole geometries in the black hole information problem. Building on recent development which suggests that information that fell into the black hole is encoded in the Hawking radiation, we point out a concrete protocol to decode the information by performing a complicated operation on the Hawking radiation called the modular flow. In Chapter 3, we propose a new type of wormhole configurations which connects the bra and the ket in the gravitational path integral that prepares a state. We point out the importance of these wormholes in resolving certain puzzles that arise in computing entropies. We discuss such wormhole configurations and their implications in two dimensional toy models of gravity. In Chapter 4, we discuss how wormholes can be used to quantify the amount of global symmetry violation in quantum gravity. This turns a qualitative old conjecture into quantitative statements. We discuss how one can compute certain entropies of Hawking radiation that could be used to quantify global symmetry violation during black hole evaporation. We also construct an explicit wormhole solution that gives a lower bound to the global charge violating amplitudes.