From black holes to baby universes in CGHS gravity
Victor Godet, Charles Marteau
Abstract
A bstract We study $$ \hat{\mathrm{CGHS}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mtext>CGHS</mml:mtext> <mml:mo>̂</mml:mo> </mml:mover> </mml:math> 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 $$ \hat{\mathrm{CGHS}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mtext>CGHS</mml:mtext> <mml:mo>̂</mml:mo> </mml:mover> </mml:math> 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.