Quantum mechanical systems with holographic duals

Abstract

This thesis is devoted to studying quantum mechanical systems with gravity duals. It is interesting to study holographic correspondence for quantum mechanical systems since we have

much more theoretical control over them compared to quantum field theories. At the same time,

gravity duals to quantum mechanical systems are quite rich as they can include black holes and

wormholes.

Chapter 2 is based on work [1] with J. Maldacena and studies aspects of gauge symmetry

in Banks-Fishler-Shenker-Susskind(BFSS) model. In the original formulation it includes gauged

SU (N ) symmetry. However, we argued that non-singlet states are separated by a finite gap from

the ground state. Therefore, gauging SU (N ) symmetry is not important at low energies.

Chapter 3 is based on paper [2] with A. Almheiri and B. Swingle. It is dedicated to studying thermalization

dynamics of systems with gravity duals. We argued that average null energy condition(ANEC)

in the bulk leads to a universal bound on the total amount of energy

exchange between two quantum systems. We study this bound perturbatively and in Sachdev-

Ye-Kitaev(SYK) model at arbitrary coupling. As a byproduct, we studied the non-equilibrium

dynamics of SYK, both analytically and numerically.

Chapter 4 is based on paper [3] with J. Maldacena. We study wormhole formation in SYK

model in real time. We start from a high temperature state, let it cool by coupling to a cold

bath and numerically solve for the large N dynamics. Our main result is that the system forms a

wormhole by going through a region with negative specific heat, taking time that is independent

of N .

Chapter 5 is based on paper [4] with I. Klebanov, F. Popov and G. Tarnopolsky. This paper

is dedicated to studying various spectral properties of large N melonic tensor models. They have

the same large N limit as SYK model, but unlike SYK they do not include disorder average. We

find the exact expression for the number of singlet states and derive various bounds on energies.