Research
I am broadly interested in several areas of theoretical physics. My primary research interest lies in the effective macroscopic description of systems near thermal equilibrium provided by hydrodynamics. I have been working on relativistic hydrodynamics, which governs the near equilibrium behaviour of Lorentz invariant systems, as well as Galilean hydrodynamics, which is more suited for applications to transport in condensed matter. My research also involves investigating hydrodynamic transport with broken symmetries, such as the breaking of translation invariance, with applications to strange metal phenomenology in high-Tc superconductors, as well as the breaking of internal symmetries, such as a global U(1) symmetry, leading to superfluidity. More recently, I have also ventured into the ultrarelativistic regime of hydrodynamics, where the underlying symmetries are given by the Carroll algebra, with potential applications to ultrarelativistic heavy-ion collisions and the quark-gluon plasma. An important tool to explore the near equilibrium behaviour and transport properties of strongly coupled quantum systems is provided by the Gauge/Gravity duality, also known as the Anti de Sitter/Conformal Field Theory (AdS/CFT) correspondence, which forms a central part of my research expertise.
A second area of interest which I am exploring is the connection between information theoretic properties of holographic quantum field theories, such as the entanglement entropy and complexity, and their description in terms of the dual gravitational picture provided by the Gauge/Gravity duality.
In the past, I have worked on inflationary cosmology to obtain model-independent constraints on correlation functions which can be observed in the near future, various aspects of supersymmetric quantum field theories, and properties of near-extremal black holes.
Please find below a very broad introduction to ideas I am currently working on or have worked on in the past.
Hydrodynamics
Hydrodynamics is the effective description governing the low energy behaviour of physical systems near thermal equilibrium. Hydrodynamics works well when one is interested in probing properties of a system at length scales much longer than the typical microscopic length scales, such as the correlation length. An example of applicability of hydrodynamics is the quark-gluon plasma, a state of matter with free quarks and gluons, produced in extremely energetic heavy-ion collisions in laboratories such as RHIC and CERN. The photo on the left shows such an event, detected by the STAR experiment at RHIC, where two Gold nuclei collided at nearly the speed of light, spewing out quarks and gluons which later hadronized as they cooled. Studying such phenomena gives us a peek into the very early universe, when the temperatures were very high and the quarks and gluons were essentially free.
Black Holes and Quantum Information
Black holes are some of the most enigmatic objects in nature. Perhaps the most common property of a black hole known to everyone is that anything that has the misfortune of falling into one gets eternally trapped. But this is not all - black holes display a plethora of phenomena which are highly non-intuitive. For instance, black holes have an entropy, and when coupled with quantum fields, can evaporate! In my past work on black holes, I have explored low energy dynamics of near-extremal black holes from the perspective of symmetries and symmetry breaking.
I am presently interested in the connections between quantum information theoretic properties of states in holographic conformal field theories, and their dual description in terms of an asymptotically anti de Sitter spacetime geometry. Examples of such quantities include the entanglement entropy and complexity. I am actively working on understanding real time dynamics and evolution of such quantum information theoretic quantities for translationally-invariant pure states in CFTs with a uniform energy density, whose holographic dual consists of AdS black holes, where part of the maximally extended geometry is cut off by an end of the world brane.
In my humble opinion, the Hubble Ultra Deep Field is one of the most beautiful images we have ever captured as humankind. Read more about it here .
Theoretical Cosmology
I am perennially interested in theoretical cosmology. Big bang cosmology, though very successful, leaves out some gaps which are difficult to explain without assuming very special initial conditions. Examples are the flatness and the horizon problems. Inflation was introduced to cure these inconsistencies in the big bang model. It proposes that the radiation dominated phase of the very early universe was preceded by another phase, when the universe underwent a very rapid exponential expansion, and hence named inflation. There is a multitude of field theoretic models which try to explain inflation. I have worked on a class of inflationary models, called single field models, in which inflation is driven by the large potential energy stored in a scalar field called the inflaton. Quantum fluctuations generated during inflation are imprinted in the cosmic microwave background radiation which fills the entire universe. My research on inflation involved deriving symmetry based constraints on the correlation functions of inflationary fluctuations. These relations between correlation functions follow as a consequence of the underlying spacetime reparametrization invariance of general relativity, and provide robust model-independent constraints on various single field models of inflation.
Chern-Simons Theories
In our four dimensional spacetime, electromagnetism is described by the Maxwell's theory. In three spacetime dimensions, it is possible to have a different theory for electromagnetism, the Chern-Simons theory, describing novel phenomena. Pure Chern-Simons theory is topological, implying that it does not have any dynamics. However, things become interesting when the theory is coupled to matter. This leads to matter behaving as anyons - particles which are neither bosons nor fermions, but obey fractional statistics. Chern-Simons theory is an important constituent in our understanding of the quantum Hall effect. My work on the Chern-Simons theory involved studying the scattering of the anyonic particles when the theory possessed supersymmetry - a symmetry that maps bosons and fermions into one another.