Office Addresses:
@ SBU: MATH-5104, Yang Institute for Theoretical Physics
Math Tower
Stony Brook University
NY - 11794-3840, USA.
@ Rutgers: E373/NHETC
Department of Physics and Astronomy
Rutgers, The State University of New Jersey
136 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA.
I am a theoretical physicist with diverse interests in quantum field theory and Physical Mathematics. For some background, please refer to the following articles:
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. Broadly, my interests include (but are not limited to):
Applications of differential/algebraic topology and category theory, to anomalies in quantum field theory, string/M-theory, and supergravity.
Topological quantum field theory; quantum computation.
Physical approaches to Cohomological quantum field theories.
String compactifications.
Supersymmetric gauge theories, and supergravity theories. Mathematical structures related to wall-crossing phenomena.
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.
Associated with the deformation class of a two-dimensional N=(0,1) SCFT, there corresponds a generalized cohomology class in the generalized cohomology theory called Topological Modular Forms (TMF), via the Segal-Stolz-Teichner conjecture. In this paper, we show that the nine-dimensional non-supersymmetric (E8)1 x (E8)1 heterotic string is T-dual to the non-supersymmetric (E8)2 heterotic string, and that the worldsheet (E8)1 x (E8)1 theory is continuously connected (i.e., homotopic) to the worldsheet (E8)2 theory via a relevant tachyon vertex operator deformation. This is used to give a physical derivation the fact that the (E8)2 theory corresponds to the unique nonzero class [(E8)2] in TMF31 with zero mod-2 elliptic genus. In particular, this means that the TMF classes of the (E8)1 x (E8)1 and (E8)2 theories coincide.
This paper gives a Quantum Field Theory (path-integral) formulation of invariants of smooth families of smooth compact four-manifolds, also known as the Family Donaldson invariants. This is carried out by unifying methods of N=2 conformal supergravity and equivariant cohomology. We derive the Cartan Model for the equivariant cohomology of (gauge transformations) ⋉ (diffeomorphisms) on the (space of connections)x(space of metrics), and write down very general actions of twisted N=2 super Yang Mills theory coupled to N=2 conformal supergravity. 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.
To appear/in preparation:
Topological Twisting of 4d N=2 Supersymmetric Gauge Theories
with G. W. Moore and R. K. Singh. (To appear.)
We discuss the topologically twisting of general 4d N=2 Lagrangian supersymmetric gauge theories using the notion of reduction of structure group on the groupoid of principal bundles on a 4-manifold associated with a homomorphism of groups.
Localization Fails, But Trees are Good Enough
with G. W. Moore. (To appear.)
We prove that the Family Donaldson invariants proposed in arXiv:2311.08394 are not renormalized and receive only tree-level contributions from the path integral, and comment on various properties of the associated u-plane path integral.
Lectures on Differential Cohomology and Topological Field Theories
with G. W. Moore. (To appear.)
Expository discusions of differential cohomology and topological field theories, with connections to recent developments in generalized symmetries.
Talks
A tale of some (topological) twisting: This talk was delivered (by Zoom) at the C.N. Yang Institute for Theoretical Physics at Stony Brook, on May 7, 2020.
Gauge Theory Phases of Five-Dimensional SCFTs: Dual perspectives from M-Theory and Type IIA String Theory: This was an in-person talk delivered at Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, on November 25, 2019. A video of the talk is available here, but suffers from some interruptions due to a malfunctioning laptop charger.
Gauge Theory Phases of Five-dimensional SCFTs: This was a 5-minute talk given as part of the TASI 2019 Student Seminars. The slides are available as a pdf.
Introduction to String Compactification and Geometry: This was a ~2.5 hr talk given as part of the YITP Advanced Graduate Theory Seminar at Stony Brook, on November 17, 2018.
Three-Dimensional Mirror Symmetry: This was a two-part talk (~2.5 hr + ~1.5 hr) given as part of the YITP Advanced Graduate Theory Seminar at Stony Brook, on April 7 and 14, 2017.
Boundary Conformal Field Theory and Surface Critical Behavior: This was a two-part talk (~2.5 hr x 2) given as part of the YITP Advanced Graduate Theory Seminar at Stony Brook, on February 19 and 26, 2016. Notes for these seminars are available as a pdf.
Anomaly Inflow in M-Theory and Horava-Witten Theory: This was my Ph.D. Candidacy Exam talk for joining the C.N. Yang Institute for Theoretical Physics at Stony Brook, on December 01, 2015. This was essentially a low-energy supergravity-based review of the work of Freed, Harvey, Minasian, Moore, and Harvey, Minasian, Moore, the Horava-Witten model, and some related applications.
Anomalous Quantum Hall Effect: This was a talk give as part of the Stony Brook Graduate Seminar on AMO/Cond-Mat Physics, and was an exploration of the anomalous quantum hall effect. Lecture slides for this talk are available as a pdf.
Strongly-Coupled Quark Gluon Plasma and the AdS/CFT Correspondence: TThis was a talk give as part of the Stony Brook Graduate Seminar on Nuclear/Particle Physics on November 9, 2015, and was a light exposition (largely for a non hep-th audience) of methods of AdS/CFT as used to describe the strongly-coupled phase of the quark gluon plasma, particularly the famed computation of the shear viscoty-to-entropy density ratio. Lecture slides for this talk are available as a pdf.
Notes
These are mostly expository, and mostly incomplete. Errors are entirely my own.
Lectures on Seiberg-Witten Theory: based on lectures by Stefano Cremonesi. Unfortunately these notes have typos. Use at your own risk. [Last updated in 2016!]
