Aspects of quantum gravity from low dimensions

Abstract

This thesis investigates two active research directions motivated by quantum gravity: ensemble holography in three-dimensional exotic gravity theories, and BPS spectra of superconformal quantum-mechanical models defined on singular target spaces. The first part concerns the ensemble holography conjecture in three dimensions. We review basic aspects of AdS3/CFT2 and motivate the said proposal, which may provide a conceptual resolution of longstanding puzzles in three-dimensional gravity, most no- tably the non-factorization of gravitational partition functions. We test this generalized holographic conjecture in a class of simplified "exotic gravity" models based on abelian Chern-Simons theory in the bulk and putatively dual to finite ensembles of rational CFTs. The conjecture seems to be consistent for certain choices of ensemble, provided that the bulk path integral includes additional "exotic" wormhole contributions. In the Chern- Simons description, these contributions are modeled by condensation surface defects. The second part is devoted to superconformal quantum mechanics (SCQM), BPS spectra, and the superconformal index. We motivate this subject through its relation to extremal black-hole physics. In particular, SCQM with D(2, 1; 0) symmetry arises in a certain scaling limit of the...