Research

I work on semiclassical aspects of quantum gravity and holographic duality. Holography describes an equivalence between a theory of quantum gravity and a lower-dimensional quantum theory without gravity. The central idea of the correspondence is that gravity should emerge from the degrees of freedom in the dual theory. I'm interested in understanding the fundamental rules and holographic nature of quantum gravity, and I want to know how these rules constrain the theory in the semiclassical regime. I mainly study these questions in exactly solvable models toy of quantum gravity within the framework of AdS/CFT, but I am also exploring them in greater generality using gravitational path integrals.

Below, you can find brief descriptions of several aspects of my work in quantum gravity.

Gravitational Thermodynamics

Probing thermal and microstate structure using gravitational path integrals

The gravitational path integral is a tool used to study the thermodynamics of gravitational systems and probe the microstate structure of black holes. Semiclassically, computing one involves finding certain classical solutions of general relativity and comparing their on-shell actions to determine the dominant phase. It is still an open problem to decide which solutions should be considered: I'm interested, in particular, in the extent to which complex geometries could play a role in black hole thermodynamics. Complex solutions have figured prominently in my work with Maciej Kolanowski on spin-refined partition functions, which probe features of the microstate structure in holographic theories. They are also the focus of an ongoing project to study fixed-area saddles with nonzero charge and angular momentum.

Heavy States in AdS₃/CFT₂

The unbearable lightness of being heavy: probing heavy states with light fields

A universal feature of gravity is that at high energies, almost any localized object will form a black hole. A complete understanding of this behavior in quantum gravity is still elusive, but semiclassically we can describe black holes by thermal states. One way to study such states is to ask how very light probe fields would behave in the vicinity of a heavy object. This story is surprisingly rich in (2+1)-dimensional AdS gravity, which has no propagating degrees of freedom and no local backreaction, but nevertheless admits black hole solutions called BTZ geometries above a certain threshold mass. Below the BTZ threshold, these solutions describe massive point particles that source a conical defect in the spacetime.

In a solo work generalizing a paper with David Berenstein and Frazier Li, I explored holographic correlators in defect and BTZ backgrounds. By matching the bulk and boundary correlators nonperturbatively, I extracted universal CFT data giving the expectation values of an infinite family of two-particle states exchanged between the light and heavy state.

Causality in Holography

A wild goose chase to save causality and understand holographic encoding

In AdS/CFT, the equivalence of bulk and boundary physics raises questions about whether one can violate causality on the boundary by taking a shortcut through the bulk. Such shortcuts are ruled out by the Gao-Wald theorem, which shows that under reasonable assumptions, points not causally related on the boundary cannot be causally related in the bulk. Together with David Berenstein, I re-examined this problem in light of the nonlocal encoding of bulk information on the boundary. The animation shows a race between a pulse of light in the bulk (the "hare," red) and a light front sent along the boundary (the "tortoise," green), along with the boundary subregion (maroon) that encodes the bulk point. We showed that although the encoding region itself can move faster than light, part of the boundary light front always remains within the encoding region as it moves, preserving boundary causality.

Ultracold Molecules

The coolest Atomic and Molecular Optics lab in New York

As an undergraduate at Columbia, I worked on AMO physics in Sebastian Will's group. The Will Lab studies ultracold gases of atoms and molecules that form Bose-Einstein condensates (BECs), which display quantum behavior on macroscopic scales. The lab has control over the quantum states of individual atom and the interactions between them, as well as the ability to form dipolar molecules with long-range interactions. These tools allow the group to gain insight into problems in many-body physics and explore novel quantum phases of matter.

I joined the Will Lab in its early days, and much of my work went towards building up the lab. I built diode lasers, aligned spectroscopy cells, and designed components using CAD and a 3D printer. I simulated and designed a Zeeman slower, which cools atoms and passes them to an atomic trap. I also wrote the code for an early version of the imaging and data analysis software, which takes a sequence of absorption images of an ultracold gas cloud, fits the data to a model, and predicts the cloud's temperature and phase-space density.