Study of the AdS${}_2$/CFT${}_1$ Correspondence with the Contribution from the Weyl Anomaly

Abstract

In this paper we will consider the Almheiri-Polchinski model of the AdS${}_2$ back reaction coupled with Liouville field, which is necessary for quantum consistency. In this model, the Liouville field is determined classically by a bulk conformal transformation. The boundary time is also reparametrized by this transformation. It is shown that the on-shell action on the boundary for the gravity sector is given by a bulk integral containing the Liouville field. This integral stems from Weyl anomaly and is SL(2,R) invariant. A prescription is given for computing correlation functions of the operators dual to massless scalars. The generating function of the correlation functions of these operators is given by a sum of matter action and the bulk integral containing the Liouville field. The latter integral leads to extra contributions to $n(\ge 6)$ point functions.

18 pages

References in corpus (2)

• Comments on the Sachdev-Ye-Kitaev model
• Chaos in AdS${}_2$ holography

Cited by in corpus (1)

• Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models