Abstract
It has been shown recently by Saad, Shenker and Stanford that the genus expansion of a certain matrix integral generates partition functions of Jackiw-Teitelboim (JT) quantum gravity on Riemann surfaces of arbitrary genus with any fixed number of boundaries. We use an extension of this integral for studying gas of baby universes or wormholes in JT gravity. To investigate the gas nonperturbatively we explore the generating functional of baby universes in the matrix model. The simple particular case when the matrix integral includes the exponential potential is discussed in some detail. We argue that there is a phase transition in the gas of baby universes.
Highlights
It has been shown by Saad, Shenker and Stanford [1] that the genus expansion of a certain matrix integral generates the partition functions of Jackiw-Teitelboim (JT), [2,3], quantum gravity on Riemann surfaces of arbitrary genus with an arbitrary fixed number of boundaries
It is shown in [1] that an important part of JT quantum gravity is reduced to computation of the Weil-Petersson volumes of the moduli space of hyperbolic Riemann surfaces with various genus and number of boundaries for which Mirzakhani [4] established recursion relations
The generating functional for the correlation functions of the boundaries of the Riemann surfaces is considered in JT gravity and in matrix theory
Summary
It has been shown by Saad, Shenker and Stanford [1] that the genus expansion of a certain matrix integral generates the partition functions of Jackiw-Teitelboim (JT), [2,3], quantum gravity on Riemann surfaces of arbitrary genus with an arbitrary fixed number of boundaries. Β n ; γ) is the double scaling (d.s.) limit of the correlation function in a matrix model with the spectral curve mentioned above. This form of the curve was obtained in [1] by computing the JT path integral for the disc. Take the double scaling limit introducing the parameter γ and obtain the relation between JT gravity and the matrix model in terms of the generating functionals: d.s. lim Gmatrix (J) ≃ Zgrav (J; γ).
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