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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 using such models to non-perturbatively construct ${N}{=}2$ and ${N}{=}4$ JT supergravity theories, the latter of which is new., Comment: 42 pages, 5 figures

A random matrix model definition of a family of ${\cal N}{=}1$ supersymmetric extensions of the Virasoro minimal string of Collier, Eberhardt, M\"{u}hlmann, 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. For two of the models the volumes vanish to all orders in the perturbative topological expansion. This amounts to a prediction for expected related computations in 3D gravity and 2D dilaton gravity., Comment: 7 pages, 4 figures, 1 trumpet. v2: Refs added, discussion improved. Supplemental Material section added with computations of new quantum volumes. v3: bibtex error fixed

The model of two dimensional quantum gravity defining the "Virasoro Minimal String", presented recently by Collier, Eberhardt, M\"{u}hlmann, 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., Comment: 12 pages, 6 figures, one trumpet

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., Comment: 10 pages, 6 figures

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 minimal 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., Comment: 4 main pages, 2 supplemental material pages, 4 figures, 1 trumpet (v3: Complete description in terms of component minimal models for all sectors achieved! New exact formulae presented.)

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., Comment: A quick read at 10 double-spaced pages (plus bibliography). Essay written for the Gravity Research Foundation 2022 Awards for Essays on Gravitation. (Honorable Mention awarded.)

It is shown that the distribution of the lowest energy eigenvalue of the quantum completions of Jackiw-Teitelboim gravity is completely described by a non-linear ordinary differential equation (ODE) arising from a non-perturbative treatment of a special random Hermitian matrix model. Its solution matches the result recently obtained by computing a Fredholm determinant using quadrature methods. The new ODE approach allows for analytical expressions for the asymptotic behaviour to be extracted. The results are highly analogous to the well-known Tracy-Widom distribution for the lowest eigenvalue of Gaussian random Hermitian matrices, which appears in a very diverse set of physical and mathematical contexts. Similarly, it is expected that the new distribution characterizes a type of universality that can arise in various gravity settings, including black hole physics in various dimensions, and perhaps beyond. It has an association to a special multicritical generalization of the Gross-Witten-Wadia phase transition., Comment: 4 pages, 2 figures (plus Supplemental Material with 5 figures)

It is proposed that a complete understanding of two-dimensional quantum gravity and its emergence in random matrix models requires fully embracing {\it both} Wigner (statistics) and 't Hooft (geometry). Using non-perturbative definitions of random matrix models that yield various JT gravity and JT supergravity models on Euclidean surfaces of arbitrary topology, Fredholm determinants are used to extract precise information about the spectra of discrete microstates that underlie the physics. A core result of the computations is that in each case, the (super) Schwarzian spectrum seen at leading order is only an approximation to a new kind of spectrum that is fundamentally discrete. It is further argued that the matrix models point to a {\it single} distinguished copy of the discrete spectrum that characterizes the holographic dual of the Lorentzian (super) gravity theory. These facts suggest that the factorization puzzle is entirely resolved since the discrete spectrum underlying the Schwarzian can have a sensible quantum mechanical origin in a single theory, without an appeal to an ensemble. It is argued that more generally, double-scaled matrix models contain information about both the Lorentzian and Euclidean approaches to quantum gravity. The former comes from the Wignerian approach while the latter from the 't Hooftian 1/N topological expansion., Comment: 54 pages, 39 multi-component figures, 8 tables, at least two puns, 1 trumpet. V2: Discussion clarified, sharpened, and otherwise improved. References added. Note added about a recent paper

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., Comment: 19 pages, 13 figures, 1 trumpet v2: Clarifying remarks made about a class of solutions

A large class of two dimensional quantum gravity theories of Jackiw-Teitelboim form have a description in terms of random matrix models. Such models, treated fully non-perturbatively, can give an explicit and tractable description of the underlying ``microstate'' degrees of freedom. They play a prominent role in regimes where the smooth geometrical picture of the physics is inadequate. This is shown using a natural tool for extracting the detailed microstate physics, a Fredholm determinant ${\rm det}(\mathbf{1}{-}\mathbf{ K})$. Its associated kernel $K(E,E^\prime)$ can be defined explicitly for a wide variety of JT gravity theories. To illustrate the methods, the statistics of the first several energy levels of a non-perturbative definition of JT gravity are constructed explicitly using numerical methods, and the full quenched free energy $F_Q(T)$ of the system is computed for the first time. These results are also of relevance to quantum properties of black holes in higher dimensions., Comment: 6 pages, 2 figures, 1 trumpet...many microstates

The quenched free energy, $F_Q(T){=}{-}T\langle \ln Z(T)\rangle$, of various JT gravity and supergravity theories is explored, taking into account the key non-perturbative physics that is accessible using their matrix model formulations. The leading low energy physics of these systems can be modelled by the Airy and (a family of) Bessel models, which arise from scaling limits of matrix ensembles. The $F_Q(T)$s of these models are directly computed by explicit sampling of the matrix ensembles, and how their properties are connected to the statistical mechanics of the underlying discrete spectrum of the ensembles is elucidated. Some of the low temperature ($T$) features of the results confirm recent observations by Jassen and Mirbabayi. The results are then used as benchmarks for exploring an intriguing formula proposed by Okuyama for computing $F_Q(T)$ in terms of the connected correlators of its partition function, the wormholes of the gravity theory. A low $T$ truncation of the correlators helps render the formula practical, but it is shown that this is at the expense of much of its accuracy. The significance of the statistical interpretation of $F_Q(T)$ for black hole microphysics is discussed., Comment: 23 pages, 29 multi-component figures, 1 trumpet (v2: Paper completely re-organized to include many new results and models and to correct the overall picture!) (v3: small typos corrected, reference to new results for JT free energy added.)

We study a Jackiw-Teitelboim (JT) supergravity theory, defined as an Euclidean path integral over orientable supermanifolds with constant negative curvature, that was argued by Stanford and Witten to be captured by a random matrix model in the $\boldsymbol{\beta}{=}2$ Dyson-Wigner class. We show that the theory is a double-cut matrix model tuned to a critical point where the two cuts coalesce. Our formulation is fully non-perturbative and manifestly stable, providing for explicit unambiguous computation of observables beyond the perturbative recursion relations derivable from loop equations. Our construction shows that this JT supergravity theory may be regarded as a particular combination of certain type 0B minimal string theories, and is hence a natural counterpart to another family of JT supergravity theories recently shown to be built from type 0A minimal strings. We conjecture that certain other JT supergravities can be similarly defined in terms of double-cut matrix models., Comment: 8 pages and 10 figures. v2: Corrected the computation of macroscopic loop insertions, and discussion. Most important results qualitatively unchanged

Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories., Comment: 37 pages, 12 figures. (v2: An important error was corrected, resulting in removal of a non-perturbative gap reported in v1. Refs. updated. Other minor improvements in presentation. v3: Updated to match published version.)

Aspects of the low energy physics of certain Jackiw-Teitelboim gravity and supergravity theories are explored, using their recently presented non-perturbative description in terms of minimal string models. This regime necessarily involves non-perturbative phenomena, and the inclusion of wormhole geometries connecting multiple copies of the nearly AdS$_2$ boundary in the computation of ensemble averages of key quantities. A new "replica-scaling" limit is considered, combining the replica method and double scaling with the low energy limit. Using it, the leading free energy, entropy, and specific heat are explored for various examples. Two models of particular note are the JT supergravity theory defined as a (1,2) Altland-Zirnbauer matrix ensemble by Stanford and Witten, and the Saad-Shenker-Stanford matrix model of ordinary JT gravity (non-perturbatively improved at low energy). The full models have a finite non-vanishing spectral density at zero energy. The replica-scaling construction suggests for them a low temperature entropy and specific heat that are linear in temperature., Comment: 20 pages, 12 figures, 1 trumpet (v2: discussion improved, references added)

Some recently proposed definitions of Jackiw-Teitelboim gravity and supergravities in terms of combinations of minimal string models are explored, with a focus on physics beyond the perturbative expansion in spacetime topology. While this formally involves solving infinite order non-linear differential equations, it is shown that the physics can be extracted to arbitrarily high accuracy in a simple controlled truncation scheme, using a combination of analytical and numerical methods. The non-perturbative spectral densities are explicitly computed and exhibited. The full spectral form factors, involving crucial non-perturbative contributions from wormhole geometries, are also computed and displayed, showing the non-perturbative details of the characteristic `slope', `dip', `ramp' and `plateau' features. It is emphasized that results of this kind can most likely be readily extracted for other types of JT gravity using the same methods., Comment: 23 pages, 35 figures (!), one trumpet and some saxophones; v2: Extra subsections added with more results and techniques for understanding spectral densities, remarkable confirmation (and extension) of a formula of Stanford and Witten, and identification of instanton corrections. New detailed results at smaller hbar included. Improvements to figures; v3: Improved discussion

It is proposed that a family of Jackiw-Teitelboim supergravites, recently discussed in connection with matrix models by Stanford and Witten, can be given a complete definition, to all orders in the topological expansion and beyond, in terms of a specific combination of minimal string theories. This construction defines non-perturbative physics for the supergravity that is well-defined and stable. The minimal models come from double-scaled complex matrix models and correspond to the cases $(2\Gamma{+}1,2)$ in the Altland-Zirnbauer $(\boldsymbol{\alpha},\boldsymbol{\beta})$ classification of random matrix ensembles, where $\Gamma$ is a parameter. A central role is played by a non-linear `string equation' that naturally incorporates $\Gamma$, usually taken to be an integer, counting e.g., D-branes in the minimal models. Here, half-integer $\Gamma$ also has an interpretation. In fact, $\Gamma{=}{\pm}\frac12$ yields the cases $(0,2)$ and $(2,2)$ that were shown by Stanford and Witten to have very special properties. These features are manifest in this definition because the relevant solutions of the string equation have special properties for $\Gamma{=}{\pm}\frac12$. Additional special features for other half-integer $\Gamma$ suggest new surprises in the supergravity models., Comment: 15 pages, 9 multi-component figures, 1 trumpet v2: Discussion of perturbation theory improved. Overall presentation enhanced in various places

Recently, Saad, Shenker and Stanford showed how to define the genus expansion of Jackiw-Teitelboim quantum gravity in terms of a double-scaled Hermitian matrix model. However, the model's non-perturbative sector has fatal instabilities at low energy that they cured by procedures that render the physics non-unique. This might not be a desirable property for a system that is supposed to capture key features of quantum black holes. Presented here is a model with identical perturbative physics at high energy that instead has a stable and unambiguous non-perturbative completion of the physics at low energy. An explicit examination of the full spectral density function shows how this is achieved. The new model, which is based on complex matrix models, also allows for the straightforward inclusion of spacetime features analogous to Ramond-Ramond fluxes. Intriguingly, there is a deformation parameter that connects this non-perturbative formulation of JT gravity to one which, at low energy, has features of a super JT gravity., Comment: 14 pages, 10 figures, one JT trumpet (v4: discussion improved throughout. v3: Several new results have been added, and new discussion, including an interesting differential equation for spectral densities, and a special analysis clarifying behaviour at E=0. Corrections and overall improvements in presentation.)

Using the fact that theories of gravity with asymptotically three-dimensional anti-de Sitter geometries have dual descriptions as two-dimensional conformal field theories (CFTs), we present the first study in field theory of the thermodynamic volume of various black hole solutions. We explain in general two-dimensional CFT terms why the presence of a thermodynamic volume can render certain black hole solutions "super-entropic". Super-entropicity simply results from the fact that the Cardy formula, which gives the gravitational Bekenstein-Hawking entropy, can over-count the CFT entropy. The examples of charged Banados, Teitelbiom and Zanelli (BTZ) black holes and generalized exotic BTZ black holes are described. These observations help explain why the specific heat at constant volume can signal the instability of such solutions, as recently conjectured., Comment: 8 pages

Recent work has uncovered Schottky-like peaks in the temperature dependence of key specific heats of certain black hole thermodynamic systems. They signal a finite window of available energy states for the underlying microscopic degrees of freedom. This paper reports on new families of peaks, found for the Kerr and Reissner-Nordstrom black holes in a spacetime with positive cosmological constant. It is known that a system with a highest energy, when coupled to two distinct heat baths, can naturally generate a thermodynamic instability, population inversion, a channel for work output. It is noted that these features are all present for de Sitter black holes. It is shown that there are trajectories in parameter space where they behave as generalized masers, operating as continuous heat engines, doing work by shedding angular momentum. It is suggested that bounds on efficiency due to the second law of thermodynamics for general de Sitter black hole solutions could provide powerful consistency checks., Comment: v1:- 18 pages, multiple figures, one trumpet; v2:- 22 pages. Improved discussion (with new refs and figures), including clarification about role of Penrose processes. v3: key sign error in first law found. Strengthens definition of heat engine paths

The charged black hole of Banados, Teitelbiom and Zanelli is studied in extended gravitational thermodynamics where there is a dynamical pressure and volume. It is a simple example of a super-entropic black hole, violating the reverse isoperimetric inequality. It is proven that this property implies that its specific heat at constant volume is negative, signalling a new kind of fundamental instability for black holes. It is conjectured that this instability is present for other super-entropic black holes, and this is demonstrated numerically for a large family of known solutions., Comment: 4 pages, 1 figure, no trumpet

Certain solutions of Einstein's equations in anti-de Sitter spacetime can be engineered, using extended gravitational thermodynamics, to yield `holographic heat engines', devices that turn heat into useful mechanical work. On the other hand, there are constructions (both experimental and theoretical) where a series of operations is performed on a small quantum system, defining what are known as `quantum heat engines'. We propose that certain holographic heat engines can be considered models of quantum heat engines, and the possible fruitfulness of this connection is discussed. Motivated by features of quantum heat engines that take a quantum system through analogues of certain classic thermodynamic cycles, some black hole Otto and Diesel cycles are presented and explored for the first time. In the expected regime of overlap, our Otto efficiency formulae are of the form exhibited by quantum and classical heat engines., Comment: 24 pages, multiple figures, 1 trumpet

In the extended thermodynamics of black holes, there is a dynamical pressure and its conjugate volume. The phase structure of many of these black holes has been studied a great deal and shown to give close analogues of the phase structure of various ordinary matter systems. However, we point out that the most studied black holes in this framework, such as Schwarzschild-AdS and Reissner-Nordstrom-AdS, and various analogues in higher-derivative gravity, do not have the type of elementary degrees of freedom that play a central role in the classic models of matter. This is because they have vanishing specific heat at constant volume, C_V. As examples with non-vanishing C_V, the Kerr-AdS and STU-AdS black holes do have such degrees of freedom, and a study of C_V(T) reveals Schottky-like behaviour suggestive of a finite window of energy excitations. This intriguing physics may have useful applications in fields such as holographic duality, quantum information, and beyond., Comment: 19 pages, 7 figures, 1 trumpet

We present a new type of generalization of the Renyi entropy that follows naturally from its representation as a thermodynamic quantity. We apply it to the case of d-dimensional conformal field theories (CFTs) reduced on a region bounded by a sphere. It is known how to compute their Renyi entropy as an integral of the thermal entropy of hyperbolic black holes in (d+1)-dimensional anti-de Sitter spacetime. We show how this integral fits into the framework of extended gravitational thermodynamics, and then point out the natural generalization of the Renyi entropy that suggests itself in that light. In field theory terms, the new generalization employs aspects of the physics of Renormalization Group (RG) flow to define a refined version of the reduced vacuum density matrix. For d=2, it can be derived directly in terms of twist operators in field theory. The framework presented here may have applications beyond this context, perhaps in studies of both quantum and classical information theoretic properties of a variety of systems., Comment: 19 pages. 5 multi-component figures

We explore a fruitful connection between the physics of conformal field theories (CFTs) in d-dimensional Minkowski spacetime and the extended gravitational thermodynamics of hyperbolic black holes in (d+1)-dimensional anti-de Sitter spacetime. The CFTs are reduced on a region bounded by a sphere. We show that Renormalization Group (RG) flows between CFTs are specific thermodynamic processes in the (p,V) plane, where the irreversibility of coarse-graining flows from the ultraviolet to the infrared corresponds to the Second Law of thermodynamics, preventing heat from flowing from low temperature to high. We observe that holographic heat engines using the black holes as a working substance correspond to specific combinations of CFT flows and deformations. We construct three special engines whose net heat and work can be described in terms of changes of entanglement entropy across the sphere. Engine efficiencies emerge as simple functions of the ratio of the number of degrees of freedom of two CFTs., Comment: 23 pages, 4 figures (v3: updated to match published version.)

We extend to non-static black holes our benchmarking scheme that allows for cross-comparison of the efficiencies of asymptotically AdS black holes used as working substances in heat engines. We use a circular cycle in the p-V plane as the benchmark cycle. We study Kerr black holes in four spacetime dimensions as an example. As in the static case, we find an exact formula for the benchmark efficiency in an ideal-gas-like limit, which may serve as an upper bound for rotating black hole heat engines in a thermodynamic ensemble with fixed angular velocity. We use the benchmarking scheme to compare Kerr to static black holes charged under Maxwell and Born-Infeld sectors., Comment: 19 pages

It is shown that aspects of the extended thermodynamic properties of the Taub-Bolt-AdS spacetime in four dimensions are similar to those of the Schwarzschild-AdS black hole. In a high temperature expansion, the equations of state begin to deviate only at next-to-subleading orders. By analogy with what has been done for black holes, Taub-Bolt's thermodynamic equations are used to define holographic heat engines, the first examples of gravitational heat engines defined using a spacetime that is not a black hole. As a further comparison, the Taub-Bolt engine efficiency is computed for two special kinds of engine cycle and compared to the results for analogous Schwarzschild black hole engine cycles., Comment: 5 pages, 2 figures

The extended thermodynamics of Reissner-Nordstr\"om charged black holes in D-dimensional anti-de Sitter spacetime has a phase structure in the (T,p) plane that includes a line of first order phase transitions ending in a second order transition point. For each D>=4, properties of the critical black hole at that point are explored, motivated by the observation that in D=4 its neighbourhood plays a core role in defining a very special class of heat engines that asymptote to Carnot efficiency in the large charge limit. This new limit provides a model of a novel low-temperature thermodynamic system. The double limit of approaching the horizon while sending q large at an appropriate rate yields a fully decoupled D-dimensional Rindler spacetime with zero cosmological constant., Comment: 4 pages, 1 figure

The Carnot heat engine sets an upper bound on the efficiency of a heat engine. As an ideal, reversible engine, a single cycle must be performed in infinite time, and so the Carnot engine has zero power. However, there is nothing in principle forbidding the existence of a heat engine whose efficiency approaches that of Carnot while maintaining finite power. Such an engine must have very special properties, some of which have been discussed in the literature, in various limits. While recent theorems rule out a large class of engines from maintaining finite power at exactly the Carnot efficiency, the approach to the limit still merits close study. Presented here is an exactly solvable model of such an approach that may serve as a laboratory for exploration of the underlying mechanisms. The equations of state have their origins in the extended thermodynamics of electrically charged black holes., Comment: 5 pages, 2 figures (Essentially the version to appear in Phys. Rev. D. Discussion and computations improved and extended. Typos fixed. References added.)

We present the results of initiating a benchmarking scheme that allows for cross-comparison of the efficiencies of black holes used as working substances in heat engines. We use a circular cycle in the p-V plane as the benchmark engine. We test it on Einstein-Maxwell, Gauss-Bonnet, and Born-Infeld black holes. Also, we derive a new and surprising exact result for the efficiency of a special `ideal gas' system to which all the black holes asymptote., Comment: 16 pages, 8 figures

Further consideration is given to the efficiency of black hole heat engines that perform mechanical work via the pdV terms present in the First Law of extended gravitational thermodynamics. It is noted that when the engine cycle is a rectangle with sides parallel to the (p,V) axes, the efficiency can be written simply in terms of the mass of the black hole evaluated at the corners. Since an arbitrary cycle can be approximated to any desired accuracy by a tiling of rectangles, a general geometrical algorithm for computing the efficiency follows. A simple generalization of the algorithm renders it applicable to more general classes of heat engine, beyond the black hole context., Comment: 10 pages, 6 multicomponent figures, one trumpet; v2: typo corrected in equation (3)

We study the efficiency of heat engines that perform mechanical work via the pdV terms present in the First Law in extended gravitational thermodynamics. We use charged black holes as the working substance, for a particular choice of engine cycle. The context is Einstein gravity with negative cosmological constant and a Born-Infeld non-linear electrodynamics sector. We compare the results for these `holographic' heat engines to previous results obtained for Einstein-Maxwell black holes, and for the case where there is a Gauss-Bonnet sector., Comment: 13 pages, 4 multicomponent figures, 1 trumpet; V2: Figure captions repaired, refs added, clarifying footnote about Born-Infeld terminology added V3: numerics and figures improved, clarifying remarks made in discussion

Working in the extended black hole thermodynamics where a dynamical cosmological constant defines a thermodynamic pressure p, we study the efficiency of heat engines that perform mechanical work via the pdV terms now present in the First Law. Here the black hole itself is the working substance, and we focus on a judiciously chosen engine cycle. We work in Gauss-Bonnet-Einstein-Maxwell gravity with negative cosmological constant and, using a high temperature expansion, compare the results for these `holographic' heat engines to that of previously studied cases with no Gauss-Bonnet sector. From the dual holographic large N field theory perspective, this amounts to studying the effects of a class of 1/N corrections to the efficiency of the cycle., Comment: 18 pages, 7 multicomponent figures. One trumpet; V2: Refs added; V3: Numerics and figures improved, analysis supplemented, clarifying remarks added to discussion V4: As it appears in CQG: some improved discussion and more analytic results added. D=6 case explored more

We study the behavior of the entanglement entropy in $(2+1)$--dimensional strongly coupled theories via the AdS/CFT correspondence. We consider theories at a finite charge density with a magnetic field, with their holographic dual being Einstein-Maxwell-Dilaton theory in four dimensional anti--de Sitter gravity. Restricting to black hole and electron star solutions at zero temperature in the presence of a background magnetic field, we compute their holographic entanglement entropy using the Ryu-Takayanagi prescription for both strip and disk geometries. In the case of the electric or magnetic zero temperature black holes, we are able to confirm that the entanglement entropy is invariant under electric-magnetic duality. In the case of the electron star with a finite magnetic field, for the strip geometry, we find a discontinuity in the first derivative of the entanglement entropy as the strip width is increased., Comment: 30 pages, 15 figures; updated to match the published version; new figure added for part of the phase diagram, references updated, typos fixed, clarification and additional explanations added in the introduction and section 3

We study aspects of the extended gravitational thermodynamics for the Taub-NUT and Taub-Bolt geometries in four dimensional locally anti-de Sitter spacetime, where the cosmological constant is treated as a dynamical pressure. Attention is paid to the phase structure in the (p,T) plane, which has a line of first order phase transitions extending from the origin. We argue for a dynamical interpretation of the unstable physics in the negative specific heat region. A deformation corresponding to a dyonic Taub-NUT/Bolt system is also explored, and the effect of the deformation on the phase diagram is characterised., Comment: 22 pages; 8 multicomponent figures; one trumpet (version that appears in CQG)

In theories of semi-classical quantum gravity where the cosmological constant is considered a thermodynamic variable, the gravitational mass of a black hole has been shown to correspond to the enthalpy of the thermodynamic system, rather than the energy. We propose that this should be extended to all spacetime solutions, and consider the meaning of this extension of gravitational thermodynamics for the Taub-NUT and Taub-Bolt geometries in four dimensional locally anti-de Sitter spacetime. We present formulae for their thermodynamic volumes. Surprisingly, Taub-NUT has negative volume, for which there is a natural dynamical explanation in terms of the process of formation of the spacetime. A special case corresponds to pure AdS_4 with an S^3 slicing. The same dynamical setting can explain the negative entropy known to exist for these solutions for a range of parameters., Comment: 15 pages. Two embedded figures. One trumpet. (v3: Some sentences and layout of section 2 slightly adjusted for clarity; new section 2.3 added showing a naive integral derivation of the volume formula. Title changed to match journal version.)

It is shown that in theories of gravity where the cosmological constant is considered a thermodynamic variable, it is natural to use black holes as heat engines. Two examples are presented in detail using AdS charged black holes as the working substance. We notice that for static black holes, the maximally efficient traditional Carnot engine is also a Stirling engine. The case of negative cosmological constant supplies a natural realization of these engines in terms of the field theory description of the fluids to which they are holographically dual. We first propose a precise picture of how the traditional thermodynamic dictionary of holography is extended when the cosmological constant is dynamical and then conjecture that the engine cycles can be performed by using renormalization group flow. We speculate about the existence of a natural dual field theory counterpart to the gravitational thermodynamic volume., Comment: 15 pages, four figures, two tables, one trumpet. v2: Improvements to refs. Some clarifying remarks added. There is further exploration of the efficiency of one of the engine examples. Some improvements to discussion of relation to holography in final section. Version to appear in CQG

Holographic studies of the entanglement entropy of field theories dual to charged and neutral black holes in asymptotically global AdS4 spacetimes are presented. The goal is to elucidate various properties of the quantity that are peculiar to working in finite volume, and to gain access to the behaviour of the entanglement entropy in the rich thermodynamic phase structure that is present at finite volume and large N. The entropy is followed through various first order phase transitions, and also a novel second order phase transition. Properties of a specific heat in the neighbourhood of the critical point are computed. Behaviour is found that contrasts interestingly with an earlier holographic study of a second order phase transition dual to an holographic superconductor., Comment: 19 pages, 9 multi-component figures (v3: Section 4.1 reduced in scope due to ansatz error in earlier versions. v4: Expanded version with several more results including study of specific heat and critical exponents.)

Four dimensional gravity with a U(1) gauge field, coupled to various fields in asymptotically anti-de Sitter spacetime, provides a rich arena for the holographic study of the strongly coupled (2+1)-dimensional dynamics of finite density matter charged under a global U(1). As a first step in furthering the study of the properties of fractionalized and partially fractionalized degrees of freedom in the strongly coupled theory, we construct electron star solutions at zero temperature in the presence of a background magnetic field. We work in Einstein-Maxwell-dilaton theory. In all cases we construct, the magnetic source is cloaked by an event horizon. A key ingredient of our solutions is our observation that starting with the standard Landau level structure for the density of states, the electron star limits reduce the charge density and energy density to that of the free fermion result. Using this result we construct three types of solution: One has a star in the infra-red with an electrically neutral horizon, another has a star that begins at an electrically charged event horizon, and another has the star begin a finite distance from an electrically charged horizon., Comment: 18 pages, 2 figures. Submitted to Springer Lecture Notes: Strongly interacting matter in magnetic fields. v2: Updated references and adjusted some phrasing in the introduction

We present the results of our studies of the entanglement entropy of a superconducting system described holographically as a fully back-reacted gravity system, with a stable ground state. We use the holographic prescription for the entanglement entropy. We uncover the behavior of the entropy across the superconducting phase transition, showing the reorganization of the degrees of freedom of the system. We exhibit the behaviour of the entanglement entropy from the superconducting transition all the way down to the ground state at T=0. In some cases, we also observe a novel transition in the entanglement entropy at intermediate temperatures, resulting from the detection of an additional length scale., Comment: 21 pages, 14 figures. v2:Clarified some remarks concerning stability. v3: Updated to the version that appears in JHEP

Using holography, we study the entanglement entropy of strongly coupled field theories perturbed by operators that trigger an RG flow from a conformal field theory in the ultraviolet (UV) to a new theory in the infrared (IR). The holographic duals of such flows involve a geometry that has the UV and IR regions separated by a transitional structure in the form of a domain wall. We address the question of how the geometric approach to computing the entanglement entropy organizes the field theory data, exposing key features as the change in degrees of freedom across the flow, how the domain wall acts as a UV region for the IR theory, and a new area law controlled by the domain wall. Using a simple but robust model we uncover this organization, and expect much of it to persist in a wide range of holographic RG flow examples. We test our formulae in two known examples of RG flow in 3+1 and 2+1 dimensions that connect non-trivial fixed points., Comment: 25 pages. 12 Figures. Corrected minor typos and clarified certain results

We study the dynamics of quenched fundamental matter in $\mathcal{N}=2^\ast$ supersymmetric large $N_c$ $SU(N_c)$ Yang-Mills theory, extending our earlier work to finite temperature. We use probe D7-branes in the holographically dual thermalized generalization of the $\mathcal{N}=2^\ast$ Pilch-Warner gravitational background found by Buchel and Liu. Such a system provides an opportunity to study how key features of the dynamics are affected by being in a non-conformal setting where there is an intrinsic scale, set here by the mass, $m_H$, of a hypermultiplet. Such studies are motivated by connections to experimental studies of the quark-gluon plasma at RHIC and LHC, where the microscopic theory of the constituents, QCD, has a scale, $\Lambda_{\rm QCD}$. We show that the binding energy of mesons in the $\mathcal{N}=2^\ast$ theory is increased in the presence of the scale $m_H$, and that subsequently the meson-melting temperature is higher than for the conformal case., Comment: 17 pages, 6 figures

We study the dynamics of quenched fundamental matter in $\mathcal{N}=2^\ast$ supersymmetric large $N$ SU(N) Yang-Mills theory at zero temperature. Our tools for this study are probe D7-branes in the holographically dual $\mathcal{N}=2^\ast$ Pilch-Warner gravitational background. Previous work using D3-brane probes of this geometry has shown that it captures the physics of a special slice of the Coulomb branch moduli space of the gauge theory, where the $N$ constituent D3-branes form a dense one dimensional locus known as the enhancon, located deep in the infrared. Our present work shows how this physics is supplemented by the physics of dynamical flavours, revealed by the D7-branes embeddings we find. The Pilch-Warner background introduces new divergences into the D7-branes free energy, which we are able to remove with a single counterterm. We find a family of D7-brane embeddings in the geometry and discuss their properties. We study the physics of the quark condensate, constituent quark mass, and part of the meson spectrum. Notably, there is a special zero mass embedding that ends on the enhancon, which shows that while the geometry acts repulsively on the D7-branes, it does not do so in a way that produces spontaneous chiral symmetry breaking., Comment: 24 pages, 8 figures. Corrected typos, added comment about counterterm. To appear in JHEP