It has been conjectured that pure gravity without matter content, in three-dimensional spacetime with a negative cosmological constant, could be a complete quantum theory. One check is to compute its thermodynamic partition function as a Feynman path integral, which contains information such as the energy spectrum. The theory is also known, at least classically and perturbatively, to admit an equivalent description by a topological field theory called Chern-Simons theory.

In the work arXiv:1903.05100 [hep-th] done with my thesis adviser Professor Massimo Porrati, we performed the first direct computation of Chern-Simons path integrals on a class (the solid torus) of physical three-dimensional spacetimes. Among other things, we discovered subtleties in analytical continuations in the computations, and gave a prescription that produces the gravity partition function. Our work also found applications to subsequent works by other authors on certain other gravity theories that are conjectured to correspond to ensemble averages of conformal field theories.

Computing partition functions of candidate gravity theories defined on three-dimensional spaces that are handlebodies of arbitrary genus (think of bagels and pretzels) can tell us a lot about their quantum nature, or lack thereof.

In the work arXiv:2104.12799 [hep-th] done with my thesis adviser Professor Massimo Porrati, we computed Chern-Simons partition functions using radial quantisation on such spaces. We sliced the space along into constant-radius two dimensional surfaces, the same way we slice an onion. In this picture, the partition functions are transition amplitudes between states defined on the singular initial surface and the final surface. We found that a Wilson loop, which is the spacetime trajectory of a charged particle, shifts the holonomy of the initial state. Together with an appropriate choice of normalization, this procedure selects a unique quantum mechanical state on the constant-radius surface. Radial quantization allowed us to find the partition functions of Abelian Chern-Simons theories for handlebodies of arbitrary genus. For non-Abelian compact gauge groups, we showed that our method reproduces the known partition function on the solid torus.

It is a well-known fact that electric field can decay quantum mechanically by spontaneously producing a pair of charged particles, e.g. electron+positron.

In arXiv:2107.04561 [hep-th], in collaboration with Professor Matt Kleban and his student Hu, Xu-Yao, we studied quantum electrodynamics with massive fermions on a circle, in two spacetime dimensions. We discovered novel, previously unknown ways in which electric field decays without producing a charged pair. We performed a thorough investigation using both analytical approaches— bosonisation and the worldline formalism of field theory— and numerical lattice simulations. We made quantitative predictions of observables, in particular the decay rates and splitting of energy levels, from these different approaches, and found that they were in good agreement. Our work also settled some disputes in some parts of the literature.