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Register a new userLow Energy Thermodynamics of JT Gravity and Supergravity
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Clifford V. Johnson
Publication date
2020
fields
Physics
and research's language is
English
Authors
Clifford V. Johnson
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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.
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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.
The quenched free energy, $F_Q(T){=}{-}Tlangle ln Z(T)rangle$, 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.
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 $(2Gamma{+}1,2)$ 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.
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.
We study a series of powerful correspondences among new multi-gravity extensions of the Jackiw-Teitelboim model, multi-SYK models and multi-Schwarzian quantum mechanics, in the $rm{(A)dS_{2}/CFT}$ arena. Deploying a $BF$-like formulation of the model, we discuss the counting of the degrees of freedom for some specific classes of multi-gravity potentials, and unveil connections among a variety of apparently different models. Quantization of multi-gravity models can be then achieved from both the Hartle-Hawking no-boundary proposal, the SYK partition function and the spin-foam approaches. We comment on the SYK quantization procedure, and deepen in the appendix the quantization scheme naturally achieved in the $BF$ framework. The new multi-gravity theory hence recovered presents intriguing applications for analogue gravitational models developed for condensed matter physics, including graphene, endowed with defects and high intensity magnetic fields.
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