arXiv subjects

Harish Murali

Publications and source records attributed to Harish Murali.

8 recordsLinked to original sources

arXiv2026

What is the simplest holographic matrix model?

We study a generalization of a two-matrix model proposed by J. Hoppe in '89. At strong coupling and large $N$, we unveil an emergent area preserving diffeomorphism symmetry of this model, which allows us to completely solve it at leading order. The solution for all $n$-point connected correlators takes the form of a Witten diagram-like expansion in an emergent two-dimensional dual spacetime. We conclude with speculations about the quantization of this dual model and comment on its extensions to higher dimensions and relations to holography more broadly.

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arXiv2026

On the strong coupling limit of Yang-Mills matrix models

We study the strong coupling limit of mass deformed Yang--Mills matrix models, with the aim of understanding when the matrices become effectively commuting. The Yang--Mills interaction classically drives the matrices toward mutually commuting valleys, where the matrices can potentially be interpreted as coordinates of an emergent space. However, taking into consideration the integration measure, commutativity is not automatic since the commuting locus is entropically suppressed, and in the bosonic models with $D\geq3$ the strong coupling limit remains non-commuting. We find that fermions change this competition in a sharp way. As the number of fermionic degrees of freedom is increased, there is a critical value $\mathcal N_c=2(D-2)$, realized by the supersymmetric Yang--Mills matrix models, at which the matrices commute at strong coupling. The same critical models also exhibit universality under deformations by $O(N^2)$, or huge, operators: the normalized eigenvalue densities are insensitive to the microscopic details of the huge operators. Increasing the number of fermions beyond the critical point still gives commuting matrices, but the huge-operator universality is lost. Thus commutativity and universality are related but distinct: the matrix models with supersymmetric field content sit at the critical boundary where we have both.

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arXiv2025

(Un)solvable Matrix Models for BPS Correlators

We propose and study a family of complex matrix models computing the protected two- and three-point correlation functions in $\mathcal{N}=4$ SYM. Our description allows us to directly relate the eigenvalue density of the matrix model for ``Huge" operators with $ \Delta \sim N^2$ to the shape of droplets in the dual Lin-Lunin-Maldacena (LLM) geometry. We demonstrate how to determine the eigenvalue distribution for various choices of operators such as those of exponential, character, or coherent state type, which then allows us to efficiently compute one-point functions of light chiral primaries in generic LLM backgrounds. In particular, we successfully match the results for light probes with the supergravity calculations of Skenderis and Taylor. We provide a large $N$ formalism for one-point functions of ``Giant" probes, such as operators dual to giant graviton branes in LLM backgrounds, and explicitly apply it for particular backgrounds. We also explicitly compute the correlator of three huge half-BPS operators of exponential type and stacks of determinant operators by reducing them to the known matrix model problems such as the Potts or $O(n)$ model on random planar graphs. Finally, we point out a curious relation between the correlators of $\frac{1}{4}$-BPS and $\frac{1}{8}$-BPS coherent state operators and the Eguchi-Kawai reduction of the Principal Chiral Model in $2D$ and $3D$ correspondingly.

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arXiv2025

Universality of Heavy Operators in Matrix Models

In large $N$ theories with a gravity dual, generic heavy operators should be dual to black holes in the bulk. The microscopic details of such operators should then be irrelevant in the low energy theory. We look for such universality in the strong coupling limit of a very simple two matrix model -- the Hoppe model. Using analytics as well as Monte Carlo simulations, we show that there exists a universal black hole regime where the eigenvalue densities are given by parabolas and the correlation functions of probes in these backgrounds are completely determined by a few parameters. An important feature of strong coupling in this model is that the matrices commute and one can define joint eigenvalue distributions which also exhibit universality. These two results extend the beautiful findings of Berenstein, Hanada and Hartnoll. Not all heavy operators are universal and at strong coupling there is a sharp phase boundary between the universal and non universal regimes (Of course this should not be confused with the universality of eigenvalue spacing in matrix models). Moreover, in the non universal phase, we also find an interesting phenomenon we call Abelianization where some eigenvalues run off to infinity, reminiscent of heavy dual giant gravitons in $\mathcal N=4$ SYM.

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arXiv2024

Huge BPS Operators and Fluid Dynamics in $\mathcal{N}=4$ SYM

In the bulk dual of holography, huge operators correspond to sources so heavy that they fully backreact on the space-time geometry. Here we study the correlation function of three such huge operators when they are given by $1/2$ BPS operators in $\mathcal{N}=4$ SYM theory, dual to IIB Strings in $AdS_5 \times S^5$. We unveil simple matrix model representations for these correlators which we can sometimes solve analytically. For general huge operators, we translate these matrix model expressions into a $1+1$ dimensional hydrodynamical fluid problem. This fluid is integrable thus unveiling a novel integrable sector of the $AdS/CFT$ duality in a full fledged gravitational regime, very far from the usual free string planar regime where integrability reigns supreme. We explain how an adiabatic deformation method can be developed to yield the solution to an integrable discrete formulation of these fluids -- the rational Calogero-Moser Model -- so we can access the general three point correlation functions of generic huge $1/2$-BPS operators. Everything will be done on the gauge theory side of the duality. It would be fascinating to find the holographic dual of these matrix models and fluids.

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arXiv2023

Following Black Hole States

We study $\mathcal{N}=4$ SYM at non-integer number of colours. By varying $N$ we can continuously follow states all the way from $N=\infty$ where integrability reigns to finite $N$ where quantum gravity effects dominate. As an application we consider classically $1/16$ BPS states. Quantum mechanically, these states are generically non-supersymmetric but some special states - at special values of $N$ - become super-symmetric at the quantum level as well. They are the so-called quantum black hole states studied recently using cohomology. We write down the form of the lightest BH state at $N=2$ - and follow it in $N$, both at weak coupling and - more speculatively - at strong coupling as well. At weak coupling this state has protected dimension $Δ=19/2$ at $N=2$ and becomes a triple trace made out of Konishi and two light BPS operators at infinite $N$ with $Δ=19/2+12λ+\dots$. At strong coupling we suspect it becomes a quadruple trace with dimension $Δ\simeq 19/2+\text{integer}$.

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arXiv2022

Where is M-theory in the space of scattering amplitudes?

We use the S-matrix bootstrap to carve out the space of unitary, analytic, crossing symmetric and supersymmetric graviton scattering amplitudes in nine, ten and eleven dimensions. We extend and improve the numerical methods of our previous work in ten dimensions. A key new tool employed here is unitarity in the celestial sphere. In all dimensions, we find that the minimal allowed value of the Wilson coefficient $α$, controlling the leading correction to maximal supergravity, is very close but not equal to the minimal value realized in Superstring theory or M-theory. This small difference may be related to inelastic effects that are not well described by our numerical extremal amplitudes. Although $α$ has a unique value in M-theory, we found no evidence of an upper bound on $α$ in 11D.

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arXiv2021

The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary

The S-matrix bootstrap is extended to a 1+1d theory with $O(N)$ symmetry and a boundary in what we call the R-matrix bootstrap since the quantity of interest is the reflection matrix (R-matrix). Given a bulk S-matrix, the space of allowed R-matrices is an infinite dimensional convex space from which we plot a two dimensional section given by a convex domain on a 2d plane. In certain cases, at the boundary of the domain, we find vertices corresponding to integrable R-matrices with no free parameters. In other cases, when there is a one-parameter family of integrable R-matrices, the whole boundary represents integrable theories. We also consider R-matrices which are analytic in an extended region beyond the physical cuts, thus forbidding poles (resonances) in that region. In certain models, this drastically reduces the allowed space of R-matrices leading to new vertices that again correspond to integrable theories. We also work out the dual problem, in particular in the case of extended analyticity, the dual function has cuts on the physical line whenever unitarity is saturated. For the periodic Yang-Baxter solution that has zero transmission, we computed the R-matrix initially using the bootstrap and then derived its previously unknown analytic form.

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