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JT Supergravity, Minimal Strings, and Matrix Models

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 نشر من قبل Clifford V. Johnson
 تاريخ النشر 2020
  مجال البحث فيزياء
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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.



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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 $bolds ymbol{beta}{=}2$ 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.
103 - Clifford V. Johnson 2020
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 in volves 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.
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