Research

Overview

Recent advancements in gauge theory/gravity dualities are shedding light on black hole microstates, particularly through large-N gauge theories. Early successes in this area reproduced the Bekenstein-Hawking entropy for specific supersymmetric black holes, inspiring numerous extensions. However, meaningful insights into black hole entropy were mostly limited to index computations for 1/16-BPS black holes, which overlook the critical dynamics of strongly coupled gauge theories.

Recent work, especially with 1/16-BPS black holes in AdS_{5}\times S^{5}, has reframed the task of counting black hole microstates using supercharge cohomology, which encompasses the full spectrum of BPS operators. This method provides much richer information than index-based approaches. A key development is the classification of BPS operators into "monotone" and "fortuitous" categories. Monotone operators scale with the gauge group rank N, while fortuitous operators exist only within certain ranks.

While the large-N expansion of Yang-Mills theories, as established by ’t Hooft, has been extensively explored in planar limits—especially in N=4 super Yang-Mills theory—this approach is inadequate for understanding black hole microstates. The planar limit fails to capture the complexity of finite-N trace relations and the intricate multi-trace structures needed for non-planar regimes, which are crucial for black hole analysis.

A promising approach to studying these microstates is to incorporate the representation theory of the symmetric group. By using restricted Schur polynomials, this method has been applied in many papers to explore anomalous dimensions in N=4 super Yang-Mills theory, with the goal of extending it to heavy operators related to 1/16-BPS black holes in AdS_{5}\times S^{5}.

Current Research

1. We consider the fishnet CFT which has the following interesting features

   • The Feynman diagrams are quite simple, which may allow us to sum them all and begin investigating strong coupling. This approach has already been applied to certain correlators in the planar limit.

   • The theory is a CFT so we can try to use the ideas of bilocal holography in this setting.

This work examines the dilatation operator for operators with large R-charge and bare dimension of order N. Using restricted Schur polynomials, the goal is to compute the operator's action and identify the operators that diagonalize it, extending the concept of Gauss graph operators from N=4 super Yang-Mills theory.

2. We are calculating two-loop anomalous dimensions in the su(2∣3) sector of N=4 super Yang-Mills theory for operators of order N, which are associated with pointlike gravitons. We select fields such that ϕ_{1}∼n_{1}​, ψ_{i}∼m_{i}​, and ϕ_{j}​∼n_{j}​, with n_{1} ​≫ n_{j}​ and n_{1} ≫ m_{i}​ for j=2,3 and i=1,2. Our goal is to diagonalize the resulting matrix elements and determine whether integrability holds at two loops.

3. We investigate the possibility of a double-copy relationship between Yang-Mills-Chern-Simons theory and topologically massive gravity in 2+1 dimensions. It involves formulating both theories using the BRST formalism, which parametrizes their symmetries with ghost and anti-ghost fields. While progress has been made in the Yang-Mills-Chern-Simons theory, this work addresses the open problem of doing so for topologically massive gravity. The goal is to map the two theories via a BRST convolution, focusing on classical solutions and extending the analysis to curved spacetime.

Open Positions

I do not currently have any funded open positions or studentships. However, if you are interested in applying for externally funded positions feel free to contact me.