Research

The primary focus of my research is the study of various aspects of quantum field theories and the gauge/gravity correspondence. In my PhD I have worked on Brownian motion and entanglement entropy in the framework of holographic duality. Currently my research is mostly focussed on the new growing area of scattering amplitudes and conformal field theories. Some details about the research topics are given below.

A list of my publications can be found here : Inspire Arxiv Google Scholar

Amplitudes from Positive Geometries

Scattering amplitudes are arguably the most important observable in physics. Although Feynman diagrammatic approach is remarkably successful, it is quite clear that it's not suitable for analysing amplitudes. One of the recent novel approaches of analysing amplitudes is treating them as "differential form" instead of functions on kinematical space and identifying them as the canonical forms of certain "positive geometry" (e.g. polytopes). Couple of years back, we analysed tree-level planar diagrams in massless $\phi^4$ theory and ask if there is a positive geometry interpretation attached to such scattering amplitudes. We showed that this is indeed the case and the positive geometry is called Stokes polytope. This was introduced by Y. Baryshnikov and is quite new (less than twenty years old) even in the mathematics literature. The top form on the Stokes polytope contains information about scattering amplitude. Statements about locality, unitarity and "soft" limits become simple geometric properties of the polytope. In a recent paper we showed the lower dimensional forms in positive geometries have nice interpretation for particular situations and thus made the connection between positive geometry and Cachazo-He-Yuan formalism stronger. Recently I am exploring this framework in non-trivial backgrounds and its possible connection with holography.

Analytic Conformal Bootstrap

Conformal bootstrap is a non-perturbative technique to constrain and solve conformal field theories. This is particularly rely on two properties : operator associativity and crossing symmetry. In 80's the conformal bootstrap was implemented to solve many 2D CFTs, notably the minimal models and the Liouville field theory. For higher dimensional CFTs, it started to develop following the 2008 paper by Rattazzi, Rychkov, Tonni and Vichi. I am particularly interested in analytic bootstrap techniques particularly in the context of holography and scattering amplitudes. One advantage of these analytic approaches is, unlike numerical bootstrap unitarity doesn't play much of a role and therefore one can study non-unitary theories using them. In a paper we initiated a study of logarithmic conformal field theories which is non-unitary, using large spin bootstrap. The current goal is to apply these techniques to some condensed matter systems.

2D CFTs, Entanglement Entropy & Holography

Reconstructing bulk geometry from CFT is a fascinating program. It is believed that CFTs with large c and sparse spectrum of operators have gravity duals. There are many evidences in the literature. Recently we have shown that n-point conformal blocks factorise in "heavy-light" limit. The computations are done in the 2D CFT using monodromy method and the results have been reproduced from the 3D bulk world-line configurations. Our result is tailor-made for computing entanglement entropy of n-disjoint intervals in excited state. In a different work, we also computed EE for sine-Gordon theory both from the field theory side and the backreacted 3D bulk geometry. The results match for near marginal perturbation.

Dissipation & Holography

My thesis work is based on studying Brownian motion of heavy quark in strongly coupled medium using holography. The main focus is on dissipation at zero temperature. This has a nice physical interpretation as radiation due to accelerating charged particle (bremsstrahlung function). We have also studied Brownian motion in presence of finite charge density.

Page updated

Google Sites

Report abuse