Welcome to my homepage. I am a postdoctoral researcher at the New High Energy Theory Center at Rutgers University. I obtained a Ph.D. from Stony Brook University, where I was part of the C.N. Yang Institute for Theoretical Physics. Prior to that, I received B.Tech. and M.Tech. degrees in Electrical Engineering from IIT Kanpur.
I am a theoretical physicist with diverse interests in quantum field theory and Physical Mathematics. For some background on what Physical Mathematics is, please see the following articles:
Somewhat naively, I like to think of this pursuit more generally as the application of physics to mathematics. Over the years, seemingly disparate mathematical techniques have found their way into high energy physics and quantum/string field theory in general, and the prospects for further enthusiastic infusion of mathematics into physics are always high, so one should not compartmentialize. However, broadly, my interests include (but are not limited to):
Recently, I have been working on an extension of Donaldson-Witten Theory, aspects of M-Theory and Ramond-Ramond (RR) fields in supergravity, and line defects in three-dimensional gauge theories. In the past, I have worked on geometric engineering of five-dimensional gauge theories from M-Theory.
Prior to graduate school in physics, I worked on analog circuits as an EE undergraduate, and studied radiation conditions in electromagnetic scattering in finite-element simulations for my senior thesis, and as a master's student, I worked on nonequilibrium Green Function techniques for modeling spin field effect transistors.
We undertake the first step toward describing invariants of families of smooth 4-manifolds, using a physical approach (see this and this) to "family" Donaldson theory. Our project unifies methods of supergravity with equivariant cohomology. Specifically, we construct a model of twisted N=2 supergravity coupled to twisted N=2 super Yang Mills, which is used to make contact with an independently-derived Cartan Model for the equivariant cohomology of (gauge transformations) ⋉ (diffeomorphisms) on the (space of connections)x(space of metrics). This realizes a proposal of Moore and Witten, and is a stepping stone to realizing an earlier proposal of Donaldson.
This paper analyzes the different phases in the moduli space of rank-2 5d SCFTs obtained from M-theory at isolated toric Calabi-Yau (CY) 3-fold singularities. Different phases of the SCFTs correspond to different crepant resolutions of these singularities (which are related by flop transitions in the extended Kähler cone), but some of these correspond to non-gauge-theoretic phases, which have no known Lagrangian description. The method developed in hep-th/1812.10451 was applied to rank-2 isolated toric CY3 singularities, and maps between the gauge-theory parameters and geometric (Kähler) parameters were presented, with the match to the modified 5d N=1 prepotential of hep-th/1812.10451. Additionally, we explored various renormalization group (RG) flows in the extended parameter spaces of these theories, which frequently relate distinct geometries by flows to theories with lower flavor symmetries.
We studied compactifications of M-theory on Calabi-Yau (CY) 3-fold isolated singularities, which determine five-dimensional superconformal field theories with N=1 supersymmetry (i.e., eight real supercharges). Resolutions of these singularities lead to various "gauge-theory phases" of the SCFTs, which are studied using the fiberwise M-theory/type IIA duality. A novel Type IIA brane picture is proposed, in which the low-energy gauge theory is engineered on stacks of coincident D6-branes wrapping 2-cycles in some ALE space (of type A) fibered over a real line, and this picture is developed to give a map between the Kähler parameters of the CY3 and the Coulomb branch parameters of the field theory. From a field-theoretic viewpoint, an interesting result of this work was a proposal for a modified expression for the Coulomb-branch prepotential of 5d N=1 gauge theories, an expression that leads to integer-quantized (mixed) Chern-Simons levels in the infrared, which is consistent with the prediction from M-theory.
These are mostly expository, and mostly incomplete. Errors are entirely my own.