arXiv subjects

Clifford V. Johnson

Publications and source records attributed to Clifford V. Johnson.

At least 19 recordsLinked to original sources

arXiv2026

Fortuitous Chaos, BPS Black Holes, and Random Matrices

The ``fortuitous'' Bogomol'nyi-Prasad-Sommerfield (BPS) sector states in gauge theory have been argued to furnish a description, through holography, of generic BPS black hole microstates. They are expected to be strongly chaotic, a necessary feature to capture the black hole dynamics. This dovetails nicely with the existence of various random matrix models of JT supergravity with extended supersymmetry, within which the BPS chaos must be contained as a subsector. This paper identifies and studies a simple random matrix model that underlies all known random matrix models of JT supergravity. It is argued that it captures many essential universal features of fortuitous BPS chaos. The model is topological, naturally interpolating between the Bessel and Airy models, where the gap energy $E_0$ controls the interpolation, and seems to have a simple intersection theory interpretation.

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arXiv2026

A boundary-addition identity for Weil-Petersson volumes and their supersymmetric generalizations

We consider $V_{g,n}(\{b_i\})$, the Weil-Petersson volumes of the moduli space of Riemann surfaces of genus $g$ with $n$ geodesic boundaries of lengths $b_i$, $(i=1,...,n)$, and various ${ N}{\geq}1$ supersymmetric generalizations of them, using a framework within which they are specializations of a larger family of quantities naturally governed by the integrable KdV hierarchy. An exact boundary-addition identity is derived that directly relates $V_{g,n+1}(\{b_1,b_2,...,b_n,b\})$, for any $b$, to the corresponding $n$-boundary KdV data underlying $V_{g,n}(\{b_1,b_2,...,b_n\})$. For ordinary Weil-Petersson volumes, expansion about the special removable-cone value $b=2πi$ reproduces three known results of Do and Norbury, organizing them as the first levels of a complete hierarchy. The higher levels are naturally built from additional KdV data, which we interpret geometrically in intersection theory as a tower of $κ$-decorated volumes. Several other recursive relations in the literature are illuminated by the identity, and various new ones are derived. The cases with ${ N}=1,2$ and (small) ${N}=4$ supersymmetry are also covered by the identity, and we exhibit some of the striking special features and results arising in each case. Among many applications presented, we use the identity to uncover the intersection theory descriptions of ${N}=2$ and small ${ N}=4$ Weil-Petersson volumes.

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arXiv2026

Supersymmetric Virasoro Minimal Strings: Unified Perturbative and Non-Perturbative Treatment

There are four known ${N}{=}1$ supersymmetric Virasoro minimal string theories, naturally coming in two pairs and labeled as 0A$^\pm$ and 0B$^\pm$. We observe here that all four are naturally described in terms of solutions of an ordinary differential equation that describes certain random matrix models with positive spectra. Two new additional 0A$^-$ theories, which are unorientable, are naturally described by the framework. The formulation allows for simple computation of all perturbative amplitudes, and provides complete non-perturbative information as well. Our approach makes it clear why type 0A$^-$ can be deformed to include a gas of Ramond vertex insertions, which we fully describe, while type 0A$^+$ cannot. While it is known that the $c\rightarrow\infty$ limit reduces the 0A$^-$ and 0B$^-$ models to the familiar 0A and 0B JT supergravities of Stanford and Witten, the same limit for the plus pair reduces to non-perturbative completions of ordinary JT gravity, one of which is known. Large families of ${N}{=}2$ and ${N}{=}4$ supersymmetric analogues of the Virasoro minimal strings are also proposed and explored in detail, using the same approach.

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arXiv2026

Further aspects of Supersymmetric Virasoro Minimal Strings

A supersymmetric version of the Virasoro minimal string was defined some time ago using random matrix model techniques. Several of the special properties of the matrix model that were noted (accessible fully non-perturbatively) underlie features shared by both 0A and 0B versions of the theory. This paper develops the formalism much further, including showing how the 0A and 0B choices familiar in continuum approaches have a direct analogue in terms of building solutions of the appropriate string equations. This also illuminates several key differences between the 0A and 0B models at the level of matrix model loop observables. The natural all-orders vanishing of loops, already observed in some 0A models, translates into the same for 0B. It is also noted that the leading amplitude for a single asymptotic boundary, as well as the trumpet partition function, are characters of a 2D superconformal field theory living on the boundary of a solid torus, suggesting a 3D chiral supergravity dual. Non-perturbative results are computed as well.

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arXiv2026

$N=1$ Supersymmetry, Weil-Petersson Volume Recursion, and a Spectral Curve

The Stanford-Witten-Norbury generalization of Mirzakhani's volume recursion computes $V^{(2m)}_{g,n}(\{b_i\})$, the Weil-Petersson volumes of the moduli space of $N=1$ supersymmetric Riemann surfaces of genus $g$ with $n$ Neveu-Schwarz boundaries of geodesic lengths $b_i$ ($i{=}1,\ldots,n$), and $2m$ Ramond punctures. Recently, a spectral curve has been derived that allows their Laplace transforms $W^{(2m)}_{g,n}(\{{\hat z}_i\})$ to be computed using topological recursion. We prove that the Stanford-Witten-Norbury volume recursion is directly derivable from the spectral curve. An alternative volume recursion can also be derived from it. The difference comes from whether the Ramond information is in the initial data, or in the volume recursion's kernels. The latter invites a geometrical understanding.

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arXiv2026

Universal formulae for correlators of a broad class of models

A simple method is presented for deriving universal formulae for the correlators, frequently denoted $W_{g,n}(\{z_i\}), i=1,..n$, of a wide range of models of physical and mathematical interest. While many alternative methods exist for constructing such correlators, these formulae can be simply written in terms of one defining function and its derivatives. The method has been applied to the Airy and Bessel models, various minimal string and superstring theories, and their associated intersection theory settings, ordinary and various kinds of supersymmetric Weil-Petersson volumes, and more besides. For all these cases, their $W_{g,n}(\{z_i\})$ are just all specializations of the same universal formulae. A special variant of the method useful for ${N}{=}1$ supersymmetric cases is also presented. It allows for swift derivations of Norbury's three closed-form formulae for the volumes $V_{g,n}$ ($g{=}1,2,3$) of ${ N}{=}1$ supersymmetric Weil-Petersson volumes, and generalizations of them to a wider set of models. Moreover a new closed-form formula for the genus 4 case $V_{4,n}$ is derived. The straightforward method for how to derive such formulae for $g{>}4$ cases is described. Throughout, crucial roles are played by the underlying integrable KdV flows, as well as the Gel'fand-Dikii equation.

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arXiv2026

Ramond from Random: Weil-Petersson Volumes for Super-Riemann surfaces with NS Boundaries and R Punctures

The Weil-Petersson (WP) volumes of the (compactified) moduli space of ${N}=1$ supersymmetric Riemann surfaces with Neveu-Schwarz (NS) boundaries are frequently discussed in the literature. Such surfaces can also have marked points called Ramond (R) punctures, where the superconformal structure degenerates. Computing the volumes when these R punctures are included is more challenging for the usual differential and algebraic geometry approaches, and they are therefore less well explored. In particular, the spectral curve describing the inclusion of R punctures is apparently unknown, so far. However, the right random matrix model approach can handle the NS and~R sectors on an equal footing. Such a construction is presented, showing how to use a recently developed technique to readily compute many closed-form formulae for $V^{(2m)}_{g,n}(\{b_i\})$, the WP volumes for genus $g$ with $n$ NS-boundaries of geodesic lengths $b_i$ ($i{=}1,\ldots,n$), and $2m$ R-punctures. Several striking relations between volumes (and subsectors thereof) emerge naturally in this approach. Moreover, the hitherto missing spectral curve is presented, and its use for (re-)deriving the $V^{(2m)}_{g,n}(\{b_i\})$ is demonstrated by using topological recursion.

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arXiv2026

Non-perturbative data for Weil-Petersson volumes and intersection numbers using ordinary differential equations

Recently, a new method was introduced for computing $V_{g,1}(b)$, the Weil-Petersson volumes of the moduli space of Riemann surfaces of genus $g$ with one geodesic boundary of length $b$, various supersymmetric generalizations of them, as well as analogous quantities in intersection theory. The physical setting is the computation of a certain one-point function in a variety of models of 2D gravity for which there is a double-scaled random matrix model (RMM) description. The method combines perturbative solutions of two ordinary differential equations (ODEs), the Gel'fand-Dikii resolvent equation, and the RMM's string equation. In this paper, we extend the method to extract non-perturbative information about the $V_{g,1}(b)$ (and their analogues) that is naturally contained in the full ODEs, providing an efficient prescription for computing the transseries coefficients of the one-point correlation function, fully incorporating ZZ-brane and FZZT-brane effects, and for the first time, mixed ZZ-FZZT-effects. We use as a case study the (2,3) minimal string, computing perturbative and non-perturbative quantities, comparing them to perturbative results from topological recursion, and to results from the recent non-perturbative topological recursion framework. As a particularly powerful further application we provide general predictions for the large order in $g$ growth of $V_{g,1}(b)$, and apply them to JT gravity, finding agreement with known results, and for analogous quantities in ${N} {=} 1$ JT supergravity, proving a conjecture of Stanford and Witten. Our predictions yield new growth formulae for the cases of ${N} {=} 2$ and ${N}{=}4$ JT supergravity.

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arXiv2025

God of the Gaps: Random matrix models and the black hole spectral gap

We show that random matrix models are a natural tool for understanding the appearance of a large gap in the microstate spectrum of black holes when there is a high degeneracy of states, in a variety of settings. While the most natural context is extended supersymmetry, where the number of BPS states scales as ${\rm e}^{S_0}$, where $S_0$ is the $T{=}0$ entropy, it is a robust feature that a large gap will appear whenever there is a mechanism producing a high degree of degeneracy. In random matrix model terms, the phenomenon is simply an extreme case of eigenvalue repulsion in the effective log gas description. We exhibit several examples for illustration, starting with the simple Wishart model, continuing with extensions of it that incorporate multicritical behaviour allowing for the emergence of gravity, and culminating in constructing multicritical matrix models of ${N}{=}2$ and ${N}{=}4$ JT supergravity theories, the latter of which is new.

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arXiv2025

Weil-Petersson volumes for extended JT supergravity from ordinary differential equations

Recent work [1] produced an efficient method for computing Weil-Petersson volumes using two ordinary differential equations (ODEs) that appear naturally in double scaled random matrix models. One is the defining string equation of the model and the other is the Gel'fand-Dikii equation satisfied by the diagonal resolvent of an auxiliary Hamiltonian used to compute correlators of macroscopic loops. In concert, when applied to Jackiw-Teitelboim gravity, the recursive expansion of these two ODEs efficiently define, order by order in genus, the Weil-Petersson volumes $V_{g,1}(b)$ for bordered hyperbolic Riemann surfaces with one geodesic boundary (length $b$) and genus $g$. The method works equally well for both ordinary and ${ N}{=}1$ supersymmetric JT gravity cases. This paper explores the method to higher genus, verifying some conjectures of ref.[1], and deriving several useful recursive formulae for general use. The method is then applied to the new examples furnished by recent matrix model definitions of JT supergravity with extended supersymmetry, and several example expressions for the volumes are derived, confirming and extending ${ N}{=}2$ examples of Turiaci and Witten, and furnishing new formulae for the cases with small and large ${ N}{=}4$ supersymmetry. The prospects for extending the ODE method to the full set of $V_{g,n}(\{ b_i\})$, ($i=1,\ldots ,n$), are discussed.

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arXiv2025

Extended JT supergravity and random matrix models: The power of the string equation

A number of supersymmetric Jackiw-Teitelboim (JT) gravity theories are known to be described (in the Euclidean path integral formulation) by double-scaled random matrix models. Such matrix models can be characterized using a certain ``string equation''. It was shown recently that in extended supergravity, when the number of BPS states scales as ${\rm e}^{S_0}$, where $S_0$ is the extremal entropy, a special ansatz for the leading order solution of the string equation yields the supergravity spectrum. Somewhat miraculously, the construction showed that the functional form of the non-BPS (continuum) sector predicts the precise form of the BPS sector, showing the robustness of the supergravity/matrix-model correspondence. In this paper, we refine the analysis and show that the string equation, combined with some simple requirements on solutions, are powerful tools for constraining the spectrum of extended JT supergravity theories. We re-explore the cases of ${N}{=}2$ and (small) ${N}{=}4$ JT supergravity, and then explore the new cases of spectra from ${N}{=}3$ and large ${N}{=}4$ JT supergravity (recently derived by Heydeman, Shi, and Turiaci) showing that our approach also works naturally for (nearly) all the models. Based on this success, we conjecture that these new supergravity models also have matrix model descriptions.

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arXiv2025

Supersymmetric Virasoro Minimal Strings

A random matrix model definition of a family of ${\cal N}{=}1$ supersymmetric extensions of the Virasoro minimal string of Collier, Eberhardt, Mühlmann, and Rodriguez is presented. An analysis of the defining string equations shows that the models all naturally have unambiguous non-perturbative completions, which are explicitly supplied by the double-scaled orthogonal polynomial techniques employed. Perturbatively, the multi-loop correlation functions of the model define a special supersymmetric class of ``quantum volumes'', generalizing the prototype case, some of which are computed.

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arXiv2025

Non-Perturbative Random Matrix Model of ${\cal N}=2$ JT Supergravity

It is shown how to non-perturbatively define a random matrix model that captures key physics of ${\cal N}{=}2$ Jackiw-Teitelboim (JT) supergravity, going well beyond the perturbative topological expansion defined recently by Turiaci and Witten. A decomposition into an infinite family of certain multicritical models is derived, leading to the definition of a non-linear differential equation from which the physics may be computed. BPS states are naturally described by the model. The non-perturbative completions of the spectral densities for non-BPS multiplets are readily extracted.

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arXiv2025

A differential equation for a class of correlation kernels

A new differential equation is derived for an object ${\widehat S}(E,E^\prime,x)$, which when integrated over the appropriate range in $x$, yields the kernel $K(E,E^\prime)$ with which $n$-point correlation functions can be computed in a wide class of models. When $E{=}E^\prime$, the equation reduces to the equation for the diagonal resolvent ${\widehat R}(E,x)$ of the Schrödinger Hamiltonian ${H}{=}{-}\hbar^2\partial_x^2{+}u(x)$ that is familiar from the classic work of Gel'fand and Dikii, and which appears in many areas of physics. This more general equation may also prove to be useful in a wide range of applications. Some special cases relevant to random matrix theory are explored using analytical and numerical methods.

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arXiv2024

Specific Heats for Quantum BTZ Black Holes in Extended Thermodynamics

It was shown recently that extended black hole thermodynamics, where the cosmological constant is a dynamical variable, giving rise to a pressure $p$ and its conjugate volume $V$, can be given a natural setting in the context of braneworld models. We study the specific heat capacities $C_p(T)$ and $C_V(T)$ of the quantum version of the BTZ black hole that lives in the induced gravity theory on the brane. There are multiple branches of solutions, and we explore and characterize key features of the possible behaviour. We identify and study a critical point in the space of solutions where both specific heats diverge. In the regime of weak backreaction where we a close to an ordinary theory of gravity, the black hole is "sub-entropic", but as backreaction is increased we note that there are parts of parameter space that has regions where it is "super-entropic". While a study of the sign of the specific heats does not always show a corresponding instability (conjectured in the literature), the presence of strong backreaction makes interpretation unclear.

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arXiv2024

On the Random Matrix Model of the Virasoro Minimal String

The model of two dimensional quantum gravity defining the "Virasoro Minimal String", presented recently by Collier, Eberhardt, Mühlmann, and Rodriguez, was also shown to be perturbatively (in topology) equivalent to a random matrix model. An alternative definition is presented here, in terms of double-scaled orthogonal polynomials, thereby allowing direct access to non-perturbative physics. Already at leading order, the defining string equation's properties yield valuable information about the non-perturbative fate of the model, confirming that the case $(c{=}25,{\hat c}{=}1)$ (central charges of spacelike and timelike Liouville sectors) is special, by virtue of sharing certain key features of the ${\cal N}{=}1$ supersymmetric JT gravity string equation. Solutions of the full string equation are constructed using a special limit, and the (Cardy) spectral density is completed to all genus and beyond. The distributions of the underlying discrete spectra are readily accessible too, as is the spectral form factor. Some examples of these are exhibited.

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arXiv2022

Wigner meets 't Hooft near the black hole horizon

Recent work on Euclidean quantum gravity, black hole thermodynamics, and the holographic principle has seen the return of random matrix models as a powerful tool. It is explained how they allow for the study of the physics well beyond the perturbative expansion. In fact, a fully non-perturbative treatment naturally unites the familiar approach of summing over smooth geometries of all topologies with the statistical approach to characterizing the typical properties of a Hamiltonian. Remarkably, this leads to an explicit excavation of the underlying microstates of quantum gravity that has applications to the low temperature dynamics of a large class of black holes.

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arXiv2022

Consistency Conditions for Non-Perturbative Completions of JT Gravity

This is a careful examination of the key components of a large $N$ random matrix model method for going beyond ordinary JT gravity's topological expansion to define non-perturbative physics. It is offered as a simple and (hopefully) clear framework within which any proposed non-perturbative definition should fit, and hence be readily compared to others. Some minimal requirements for constructing consistent non-perturbative formulations are emphasized. A family of non-perturbative completions emerges from this, which includes an earlier construction. End-of-the-World branes, or simply D-branes, emerge straightforwardly in this framework and play a natural role. The many-body fermion picture of the matrix model is a key organizing motif, with many features highly analogous to a quantum black hole system, including a size that grows with the number of its microscopic constituents and a locus (the Fermi surface) beyond which quantities are traced over in order to define the physics. A formula for the thermal density matrix is proposed that allows a von Neumann form for the entropy to be written in matrix model terms.

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