I am interested in physics related to string theory, AdS/CFT duality, classical and quantum gravity, and dynamics of non-equilibrium systems.
A recurring theme in my research is thermality, various notions of entropy, and real-time dynamics.
Here are some of the topics that I am currently thinking about:
Classical chaos is associated with the butterfly effect at early times and notions of ergodicity at late times. I am interested in quantum versions of these phenomena and the intriguing mathematical structures describing them. One way to characterize early-time quantum chaos is by means of out-of-time-order correlation functions. These observables serve both as a diagnostic of black hole-like physics in quantum field theories, and as a tool to understand quantum aspects of gravity (such as shockwave scattering near a black hole horizon) in holographic CFTs. Among other things, I am developing a simple effective field theory of this ''quantum butterfly effect'' in CFTs with many degrees of freedom. Another manifestation of chaos is a certain universal behavior of the spectral form factor, which I work to understand using conformal field theory and effective field theory methods.
The fact that a low energy sector of the Sachdev-Ye-Kitaev model admits a simple holographic description is tied to a disorder average over random coupling constants. Much remains to be understood about the role of ensemble averaging in AdS/CFT. What notions of ensemble averaging are useful in higher dimensions and what role do they play in holography? What do the gravitational path integral and the gravitational replica trick teach us about spacetime emergence and wormholes? Replica symmetry breaking and spin glass order are crucial characteristics of some models with random disordered interactions -- can we understand these phenomena in holography?
Hydrodynamics provides a coarse-grained description of quantum field theory in local thermal equilibrium. It has only recently become clear how to think about hydrodynamics as a genuine effective field theory of low-energy degrees of freedom. We found that universal emergent symmetries play an important role in constraining such an effective theory: they make it possible to write an effective action for dissipative hydrodynamics and explain the emergence of the entropic arrow of time in fluid systems. These symmetry principles have a rich mathematical structure described by a cohomological supersymmetry, aspects of which are known from topological quantum field theory and from the theory of stochastic differential equations. I am interested in understanding more about this structure, and in particular what we can learn from it about dissipation and Hawking physics in gravity.
Based on the Ryu-Takayanagi formula and many subsequent developments it is known that correlations and quantum entanglement between CFT degrees of freedom provide a crucial ingredient for having a dual description in terms of semi-classical gravity. I have worked on furthering our understanding of the precise mechanism by which a (quantum) gravitational description emerges from CFT degrees of freedom. For example, understanding quantum corrections to the classical relation between entropy and area is important, as demonstrated by recent developments regarding a solution to the black hole information paradox. I am also interested in identifying other quantum information theoretic quantities that teach us interesting new things about gravity, holography, and black holes.