My PhD Thesis

Aspects of Quantum Gravity, Holography and Entanglement

My doctoral thesis was highly praised by the examiners. The comments of the examiners include

• "This thesis contains very high quality work at the frontiers of quantum field theory, general relativity and gauge-gravity duality. The issues addressed are of fundamental interest and the results are solid. The papers included here have al- ready made a significant impact in the field. It is particularly noteworthy that the candidate has published a single author paper in a top journal [...] In my opinion, this thesis far exceeds the expectations from a Ph.D. thesis in this field."

• "Upamanyu Moitra’s thesis is a compendium of several interesting results. I believe it is worth three Ph.D. theses [...] [T]his thesis contains three different important results [...]"

• "The research is original, of high quality [...] Upamanyu has written a good thesis"

You can read the different sections of my PhD thesis here:

• Acknowledgements

• Table of Contents (List of Publications and Figures)

• Chapter 1: Introduction

• Chapter 2: Rotating Black Holes and Jackiw-Teitelboim Gravity

• Chapter 3: Fluid Dynamics for Near-Extremal Black Branes

• Chapter 4: The Strong Cosmic Censorship Conjecture in Two Dimensions

• Chapter 5: Quantum Information-Theoretic Measures in Gauge Theories and Duality

• Chapter 6: Coda

• Appendix: Conventions and Useful Formulæ

• Bibliography

Abstract of the Thesis

I explore topics in quantum gravity, holography and quantum entanglement in this thesis and obtain several novel results in these topics.

This thesis shows why Jackiw-Teitelboim (JT) gravity reproduces the correct low-temperature thermodynamic behaviour of nearly extremal black holes, resolving a puzzle in the literature. The arguments are shown true for black holes in general supergravity theories with a near-horizon AdS2 geometry and the associated SL(2, R) isometry, including rotating black holes. These arguments are explicitly verified for some general examples of rotating black holes in four and five dimensions. This work could have interesting phenomenological implications.

A careful analysis in this thesis shows that, contrary to previous expectations, one can formulate a fluid-gravity correspondence even in the regime where the temperature is the smallest scale. Surprisingly, the constitutive relations become non-local in time beyond first order. The analogues of the hydrodynamic modes are obtained from first order fluid dynamics. In spite of the non-locality, the validity of a sensible perturbation theory is demonstrated. A novel feature of the time evolution of near-extremal fluid dynamics is established. Some time-independent solutions in an extremal background are also studied in relation to the attractor mechanism – two classes of bulk solutions are found that are dual to forced fluids.

The question of the validity of the strong cosmic censorship conjecture is studied for AdS2 black holes. For neutral probe scalar fields, the conjecture is shown to be severely violated; a similar violation is also demonstrated for charged scalar fields. This work explains why some near-extremal black holes violate the conjecture, as pointed out in some recent studies.

The continuum-limit behaviour of the classical term of entanglement entropy in gauge field theories is explored and it is shown that the classical contributions to certain quantum information-theoretic quantities vanish in the continuum limit, in a wide class of gauge theories. Furthermore, the general behaviour of the algebra of observables in gauge theories under electric-magnetic duality is examined. In some special cases, the entanglement spectra on two sides of the duality are argued to coincide. Two different definitions of centres are argued to give identical answers for some ultraviolet-safe quantities in the continuum limit via duality, in general.