I have been working since Summer 2020 with Prof. Iain Stewart on topics related to Glauber SCET. Our particular focus has been the Regge limit of 2-to-2 gluon scattering, which can be described in the language of SCET using Glauber exchange diagrams.

Many interesting features of Regge amplitudes can be extracted from the SCET picture. For example, two-loop Regge amplitudes arise from one- and two-Glauber exchange diagrams, and unitarity constrains the sum of these such that loops in the soft sector may be “traded out” for much simpler Glauber loops. This allows a simple calculation of the two-loop Regge trajectory and explains the previously puzzling appearance of the soft cusp anomalous dimension at this loop order. See this paper for details.

Currently, we are looking at three-Glauber exchange diagrams to describe an NNLL evolution equation for Regge amplitudes. See this talk for details.

Articles:

• Anomalous Dimensions from Soft Regge Constants
• A Collinear Perspective on the Regge Limit

Invited Talks:

• A NNLL Evolution Equation for Regge Amplitudes [World SCET 2022, Bern]

I have been working since Summer 2022 on various aspects of the analytic Langlands program as laid out here, here, and here. The analytic Langlands program reformulates the original geometric Langlands program in terms of differential operators on the moduli space of G-bundles over a smooth projective algebraic curve X.

It was realized long ago by Kapustin and Witten that the (Betti version of the) geometric Langlands program was most naturally interpreted in the context of electric-magnetic duality in twisted \mathcal{N} = 4 super-Yang-Mills, which itself manifests as a duality between topological A-models and B-models when placed on X \times \mathbb{R}^2. Recently, this formalism was extended to the analytic Langlands program.

I am investigating particular sections on the moduli space of G-bundles (”conformal blocks”) that arise in certain chiral vertex algebra constructions. A prototypical example is conjectured by Gaiotto here and proven by us in an upcoming paper. Further avenues for consideration would be extending the above chiral algebra construction to more general groups G.

Articles

• Multiplication Kernels for the Analytic Langlands Program in Genus Zero

Using brane probes and a variety of other Swampland techniques, we study the geometry of infinite-distance limits of 9d \mathcal{N} = 1 supergravity where the light tower of states predicted by the Swampland distance conjecture is not BPS. We classify these so-called non-BPS limits and provide a new approach to the String Lamppost Principle in 9d.

Articles

• Non-BPS Path to the String Lamppost

I’m interested in what the global geometry of the moduli space of vacua of an EFT coupled to gravity can say about the higher spectrum of the theory. In examples with enough supersymmetry, it is observed that the exact moduli space of vacua exhibits special loci at which enhanced gauge symmetries appear. Moreover, these loci correspond to fixed points of the action of a duality group, which can itself be thought of as a Higgsed discrete (often nonabelian) gauge symmetry.

In these examples, the duality group also acts on a lattice of electrically charged objects in the theory; by identifying a basis for this charge lattice, one identifies the different fundamental regions under the duality quotient, uplifting from the moduli space to a so-called “marked moduli space”. The marked moduli space appears to be topologically trivial (contractible), indicating that the global geometry of the original (unmarked) moduli space is somehow encoded in the spectrum of the theory. A deeper understanding of this relationship could open the door to powerful Swampland constraints.

Articles:

• Swampland and the Geometry of Marked Moduli Spaces