Abstract
We construct the most general theory of 2D Einstein-dilaton gravity coupled with U(1) gauge fields that contains all the 2-derivative and the 4-derivative interactions allowed by the diffeomorphism invariance. We renormalise the 2D action and obtain the vacuum solution as well as the black hole solution. The vacuum solution in the UV is dominated by Lifshitz2 with dynamical exponent (z = frac{7}{3} ) while on the other hand, the spacetime curvature diverges as we move towards the deep IR limit. We calculate the holographic stress tensor and the central charge for the boundary theory. Our analysis shows that the central charge goes as the inverse power of the coupling associated to 4-derivative interactions. We also compute the Wald entropy for 2D black holes and interpret its near horizon divergence in terms of the density of states. We compare the Wald entropy with the Cardy formula and obtain the eigen value of Virasoro operator (L0) for our model. Finally, we explore the near horizon structure of 2D black holes and calculate the central charge corresponding to the CFT near horizon. We further show that the near horizon CFT may be recast as a 2D Liouville theory with higher derivative corrections. We study the Weyl invariance of this generalised Liouville theory and identify the Weyl anomaly associated to it. We also comment on the classical vacuum structure of the theory.
Highlights
It has been more than two decades since the discovery of the celebrated AdS/CFT correspondence [1]–[3]
We construct the most general theory of 2D Einstein-dilaton gravity coupled with U(1) gauge fields that contains all the 2-derivative and the 4-derivative interactions allowed by the diffeomorphism invariance
In the present work we extend the notion of 2D Einstein-Maxwell-Dilaton gravity by incorporating the most general form of quartic interactions allowed by the diffeomorphism invariance
Summary
It has been more than two decades since the discovery of the celebrated AdS/CFT correspondence [1]–[3]. The authors in [37] consider the JT gravity model minimally coupled to the U(1) gauge fields and study the holographic stress tensor and the central charge [6, 7, 37, 40]–[44] for the boundary theory. We discuss the Wald entropy [72]–[74] for 2D black holes and observe that the Wald entropy diverges near the horizon due to the presence of higher derivative interactions. We interpret these divergences in terms of the density of states [75]–[77].
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