My Research
Research Projects
Below you can find a brief (technical) summary of my most recent papers, along with a link to the article.
Research Overview
A Bird's Eye View: Broadly speaking, I work at the intersection of high-energy and mathematical physics. Where helpful, I often borrow tools from, on the one hand, algebraic geometry and random matrix theory or on the other, from condensed matter and quantum information theory. These include for example intersection theory on the moduli space of curves, large N matrix models, measures of entanglement entropy or von Neumann algebras.
My Main Direction: Most of my research focuses on the idea of holography. At its core, it posits an exact equivalence between certain quantum field theories and theories of quantum gravity. This equivalence forces us to question some of our most fundamental assumptions about the very nature of spacetime: it must somehow emerge from the non-geometric degrees of freedom of the field theory.
The Big Questions Now: But how does holography precisely work? Can we identify the underlying mechanism which makes manifest how holographic theories (which are usually large N gauge theories) encode theories of quantum gravity? If so, could we hope to derive something like the AdS/CFT correspondence - our best understood example of holography?
Some First Answers: I have spent the past few years trying to answer these questions, starting from an old idea due to 't Hooft and later refined by Gopakumar. We have begun to flesh out how the Feynman diagram expansion of gauge theory observables manifestly translates into a sum over 2d surfaces. These 2d surfaces are the worldsheets of an emergent dual closed string, our best description for a complete theory of quantum gravity.
My collaborators and I have by now succeeded in deriving the simplest gauge/string duality, which relates certain matrix integrals to topological strings. Moreover, this example captures a topological subsector of the full AdS/CFT correspondence, thus paving a way forward towards a better understanding of how holography fundamentally works in more generality.
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For over fifty years, the string dual to the simplest gauge theory - the one-matrix model - has remained mysterious. We provide a concrete worldsheet theory for any interacting one-matrix integral. It manifestly reproduces all single-trace correlators, to all orders in 1/N and all orders in the ‘t Hooft couplings. The string theory is a B-twisted Landau-Ginzburg model, coupled to 2d topological gravity. Matrix model observables are explicitly mapped to computable integrals over the moduli space of Riemann surfaces.
This interactive notebook allows you to specify the matrix model potential and the correlator you would like to compute: it will derive the exact dual integrand on moduli space and perform the integral.
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Moving beyond matrix models, we explore the ideas of open-closed-open triality in the context of twisted holography. Starting from determinant correlators in the boundary theory, we derive the full open string field theory on giant graviton branes in the back-reacted geometry - an open string diagnostic of the emergent spacetime.
We show how a class of matrix model correlators very generally define a notion of discrete volumes of the moduli space of Riemann surfaces, and obey a Mirzakhani-like recursion relation. In a certain limit, these universally asymptote to the volumes of Kontsevich. For the DSSYK matrix integral, these define a discrete q-deformed analog of the Weil-Petersson volumes.
The fruit of several years of work, it provides a precise realization of 't Hooft's vision as to how gauge theory Feynman diagrams encode the worldsheet of a dual closed string theory for the 1/2 SUSY sector of N=4 Super Yang-Mills. Demonstrated open-closed-open triality of this subsector of the AdS/CFT correspondence in terms of open strings on giant graviton branes.
We show there exists two types of open/closed string duality underlying holography. By considering two stacks of branes, we derive two dual open string descriptions for the same closed string theory by exactly integrating out either stack. From it, we map a general 2-matrix chain onto the Imbibo-Mukhi matrix integral for the c = 1 string at self-dual radius. This establishes a novel correspondence between matrix model traces and tachyon vertex operators in the c = 1 string.
Matched the Bekenstein-Hawking entropy of the de-Sitter cosmological horizon by counting certain energy eigenstates of a $T\bar{T}+\Lambda_2$ deformed holographic CFT. The solvability of the deformation plays a role akin to BPS-protection in the celebrated Strominger-Vafa derivation.
Gave previously unobtainable, exact in N answers for arbitrary k-point correlators of (inverse) determinants in random matrix theory, including within the novel regime of k>N. Physically, these corresponds to observables built out of (ghost) FZZT branes (in the minimal string context)/dual giant gravitons (in AdS/CFT).
Proposed a curved spacetime generalization of the TTbar-deformation by relating the flow equation to a radial Wheeler-de-Witt equation and identifying the deformed partition function as an annulus amplitude in 3d topological gravity.
In first quantized theories, such as worldsheet string theory, the physical space is the target space (and not the ”base space”/worldsheet). Using the theory of von Neumann algebras, we defined a novel entanglement measure to describe partitions of the target space by identifying a relevant subalgebra of operators.
Demonstrated that the joint JbarT , JTbar & TTbar deformations of two-dimensional quantum field theories could be written as coupling the original theory to a mixture of topological gravity and gauge theory.
In the search of quantum gravity models with a finite dimensional Hilbert space, we explored how a continuous matrix integral captures the physics of N^2 Ising spins in the large N limit, a phenomenon known in the condensed matter literature as "spin softening". Known phase transitions in the matrix description predicted novel phases above the onset of glassiness, diagnosed by the connectedness of the eigenvalue distribution.
Constructed a concrete realization of “It-from-Qubit” by deriving a holographic matrix quantum mechanics from a large N, non-local qubit system.
Derived UV-finite bulk entanglement entropy in two-dimensional string theory from eigenvalue entanglement in the dual 0+1-dimensional “c = 1” matrix quantum mechanics. (Editor's Suggestion, PRL)
Realistic models of high-energy physics include multiple scalar fields. The nonminimal couplings induce a nontrivial field-space manifold in the Einstein frame, and they also yield an effective potential in the Einstein frame with nontrivial curvature. The ridges or bumps in the Einstein-frame potential can lead to primordial non-Gaussianities of observable magnitude. Developed a covariant formalism to study perturbations in such models and calculate the primordial bispectrum.