Most of my research is motivated by better understanding the connections between gravity and gauge fields. Currently the main directions I'm following involve:
Gravitational Collapse in AdS
Wilson Loops
Disorder in AdS/CFT.
(below you may see the respective brief descriptions).
I have other ongoing interests which involved the structure of certain supergravity solutions, proving and investigating dualities among string and field theories and localization of supersymmetric field theories as well as the role of classical and quantum chaos in AdS/CFT.
For the full list of publications please visit the link: Publications
Gravitational Collapse in AdS
Gravitational collapse is one of the fundamental dynamical processes in Einstein’s theory of general relativity. The interest in gravitational collapse in asymptotically Anti-de-Sitter (AdS) has seen a resurgence in recent years due to fundamental questions of general relativity such as vacuum stability and also as a result of motivations from the AdS/CFT correspondence. I am working in understanding this phenomena and in quantifying how it takes place. In particular in "A Kolmogorov-Zakharov Spectrum in AdS Gravitational Collapse '' we explicit computed a KZ scaling. In a collaboration involving various groups we plan to understand gravitational collapse better and frame it in the language of wave turbulence.
Ultimately, some of the techniques involved in studying the gravitational collapse in AdS could help us understand quantum turbulence from a different perspective. Turbulence is one of the most universal phenomena in physics and we expect that AdS/CFT approach to be as valid as any.
Wilson Loops
The half-supersymmetric Wilson loop in ${\cal N}=4$ is arguably the central non-local operator in the AdS/CFT correspondence. On the field theory side, the vacuum expectation values of Wilson loops in arbitrary representations of $SU(N)$ are captured by a Gaussian matrix model. At the moment, the string theory side of the AdS/CFT correspondence fails to reproduce the subleading corrections to the vacuum expectation values ("One-loop structure of higher rank Wilson loops in AdS/CFT ''). I view this as an opportunity to learn how string perturbation theory is to work on curved backgrounds with RR flux.
Disorder in AdS/CFT
Disorder is a fundamental paradigm in condensed matter physics as it provides a crucial step away from clean systems towards realistic ones. One of the most striking and ubiquitous manifestations of disorder in non-interacting quantum systems is the phenomenon of Anderson localization, where the conductivity can be completely suppressed by quantum effects. One interesting result was reported in ''The Holographic Disorder-Driven Superconductor-Metal Transition'' where we observe that the behavior of the order parameter close to the transition is not mean-field type as in the clean case, rather we find robust agreement with BKT.
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