Liouville theory and matrix models: a Wheeler DeWitt perspective

We derive explicit expressions for a specific subclass of Jackiw-Teitelboim (JT) gravity bilocal correlators, corresponding to degenerate Virasoro representations. On the disk, these degenerate correlators are structurally simple, and they allow us to shed light on the 1/C Schwarzian bilocal perturbation series. In particular, we prove that the series is asymptotic for generic weight h ∉ −ℕ/2. Inspired by its minimal string ancestor, we propose an expression for higher genus corrections to the degenerate correlators. We discuss the extension to the $$ \mathcal{N} $$ N = 1 super JT model. On the disk, we similarly derive properties of the 1/C super-Schwarzian perturbation series, which we independently develop as well. As a byproduct, it is shown that JT supergravity saturates the chaos bound λL = 2π/β at first order in 1/C. We develop the fixed-length amplitudes of Liouville supergravity at the level of the disk partition function, the bulk one-point function and the boundary two-point functions. In particular we compute the minimal superstring fixed length boundary two-point functions, which limit to the super JT degenerate correlators. We give some comments on higher topology at the end.

Section: Jhep04(2021)245mentioning

confidence: 92%

“…(9.8) JHEP04(2021)245 This is a simple proof that marking operators act as the identity operator in the fixed-length basis. 36 Multiple local marking operators are then readily accommodated by the expression:…”

Section: Jhep04(2021)245mentioning

confidence: 99%

Degenerate operators in JT and Liouville (super)gravity

Mertens

2021

“…For the case of c = 1 (b = 1) several expressions for the all-genus result are known in JHEP01(2021)073 a very concise form, see e.g. [96] for early work and [97] for a recent account.…”

Section: Jhep01(2021)073mentioning

confidence: 99%

Liouville quantum gravity — holography, JT and matrices

Mertens

Turiaci

2021

105

192

We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of SL(2, ℝ), a connection we develop in some detail. For the case of the (2, p) minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large p limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large p limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a sinh Φ dilaton potential.

“…If there is no secret mechanism to exactly cancel these contributions, they appear to be in contradiction with holography [35]. For recent work on this factorization issue, we refer to the (non-exhaustive) list of references [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52].…”

Section: Jhep07(2021)138mentioning

confidence: 99%

From black holes to baby universes in CGHS gravity

Godet

Marteau

2021

We study $$ \hat{\mathrm{CGHS}} $$ CGHS ̂ gravity, a variant of the matterless Callan-Giddings-Harvey-Strominger model. We show that it describes a universal sector of the near horizon perturbations of non-extremal black holes in higher dimensions. In many respects this theory can be viewed as a flat space analog of Jackiw-Teitelboim gravity. The result for the Euclidean path integral implies that $$ \hat{\mathrm{CGHS}} $$ CGHS ̂ is dual to a Gaussian ensemble that we describe in detail. The simplicity of this theory allows us to compute exact quantities such as the quenched free energy and provides a useful playground to study baby universes, averages and factorization. In particular we derive a “wormhole = diagonal” identity. We also give evidence for the existence of a non-perturbative completion in terms of a matrix model. Finally, flat wormhole solutions in this model are discussed.