I am currently the Quantum Initiative Fellow at the Center for the Fundamental Laws of Nature, Harvard University. My primary academic advisor is Daniel Jafferis. Prior to my days at Harvard, I pursued my graduate studies under the guidance of Shiraz Minwalla.

Primary research interest

Geometry and entanglement

Long-range entanglement in quantum field theories provides the theoretical playground for fault-tolerant quantum computation. Prototype field theory featuring such entanglement structure includes Chern-Simons gauge theory coupled to matter fields. During my graduate studies, I have extensively investigated the properties of such theories and discovered the existence of the new Higged phases. When such a theory is placed in an external uniform magnetic field, it features a non-commutative structure at all energy scales. Taking advantage of the non-commutative structure I have found an `exact’ solution for the rich band structure at non-zero chemical potential.

Through the lens of holography, geometric properties of a gravitational theory in AdS get related to the entanglement of the conformal field theories on its boundary - this fact often goes by the name of ER=EPR. During my early days at Harvard, I established a new strong-weak duality on the worldsheet of strings in AdS(3) that is closely related to ER=EPR. Essentially the duality allows one to obtain a winding condensate description of the BTZ black hole (the large black hole in AdS(3)). Utilizing such a description, I have been able to formulate an infinitesimally off-shell worldsheet technique (conceptually it is related to the Lewkowycz-Maldacena replica trick on the bulk) to calculate the thermal entropy of the blackhole from the first principle worldsheet calculation at weak strings coupling. Recently, such formalism is generalized for the application to Schwarzschild blackhole in large spacetime dimensions.

Hagedorn transition, tachyon condensation, and beyond

The winding condensate description of the strings in thermal AdS(3) mentioned above allowed the study of condensation of nearly marginal winding tachyon on the Euclidean time circle near Hagedorn temperature perturbatively directly from the worldsheet. Away from the Hagedorn temperature, the perturbation theory breaks down. At Hawking-Page temperature, I studied a specific double winding condensate CFT and conjected it to be continuously connected to the perturbative solution mentioned above as we increase the temperature.

While Hagedorn density of states is the hallmark of perturbative string theory, it has been long speculated if there exist theories with higher than the Hagedorn growth of density of states. I have shown that tensor model quantum mechanics of SYK type is a good candidate for such theories, while the gravitational dual to such quantum mechanics still remains to be found.

Additional interests

I am also facinated with the development of the non-linear machine learning techniques in recent times. In my free time I often spend hours in applying these techniques to challenging numerical problems. If you have an interesting project idea along these directions feel free to reach out to me.