AdS2 holographic dictionary
Received: October
AdS2 holographic dictionary
Mirjam Cvetic 0 2 3 4 5 6 7 8
Ioannis Papadimitriou 0 2 3 6 7 8
0 We further show that the only
1 solutions of the STU model
2 Via Bonomea 265 , 34136 Trieste , Italy
3 University of Maribor , SI2000 Maribor , Slovenia
4 Center for Applied Mathematics and Theoretical Physics
5 Department of Physics and Astronomy, University of Pennsylvania
6 Open Access , c The Authors
7 family of asymptotically AdS
8 [14] A. Castro , D. Grumiller, F. Larsen and R. McNees, Holographic description of AdS
We construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional Einstein-Maxwell-Dilaton theory that is obtained by a circle reduction from Einstein-Hilbert gravity with negative cosmological constant in three dimensions. This speci c model ensures that the dual theory has a well de ned ultraviolet completion in terms of a two dimensional conformal eld theory, but our results apply qualitatively to a wider class of two dimensional dilaton gravity theories. For each type of solutions we perform holographic renormalization, compute the exact renormalized onepoint functions in the presence of arbitrary sources, and derive the asymptotic symmetries and the corresponding conserved charges. In both cases we nd that the scalar operator dual to the dilaton plays a crucial role in the description of the dynamics. Its source gives rise to a matter conformal anomaly for the running dilaton solutions, while its expectation value is the only non trivial observable for constant dilaton solutions. The role of this operator has been largely overlooked in the literature. non trivial conserved charges for running dilaton solutions are the mass and the electric charge, while for constant dilaton solutions only the electric charge is non zero. However, by uplifting the solutions to three dimensions we show that constant dilaton solutions can support non trivial extended symmetry algebras, including the one found by Compere, Song and Strominger [1], in agreement with the results of Castro and Song [2]. Finally, we demonstrate that any solution of this speci c dilaton gravity model can be uplifted to a in four dimensions, including non extremal black holes. The four dimensional solutions obtained by uplifting the running dilaton solutions coincide with the so called `subtracted geometries', while those obtained from the uplift of the constant dilaton ones are new. ArXiv ePrint: 1608.07018
2D Gravity; AdS-CFT Correspondence; Black Holes; Space-Time Symmetries
1 Introduction and summary of results
The general solution of 2D Einstein-Maxwell-Dilaton gravity
General solution with running dilaton
General solution with constant dilaton
Extremal solution as an interpolating RG
Vacuum solutions
Uplift to four dimensions
Radial Hamiltonian formulation
Holographic dictionary for running dilaton solutions
Holographic dictionary for constant dilaton solutions
4 3D perspective
Running dilaton solutions from spacelike reduction
Constant dilaton solutions from null reduction
Conserved charges and asymptotic symmetry algebras
Running dilaton solutions
Constant dilaton solutions
Running dilaton solutions
Constant dilaton solutions
Extended symmetries from 3D embedding
A 4D subtracted geometries and Kaluza-Klein Ansatze
B Comparison with [2] and [3]
Introduction and summary of results
Despite the plethora of gravity and string theory backgrounds that contain an AdS2 region,
arising for example in the near horizon limit of near extremal black holes [4] or at the
infrared of holographic renormalization group (RG) ows with nite charge density [5], AdS2
holography remains less understood than its higher dimensional cousins. Paradoxically,
one of the main reasons is that it is apparently trivial: pure AdS2 gravity does not allow
nite energy excitations [6].
Nevertheless, AdS2 holography has been studied extensively [3, 4, 7{21] and has been
used to count the microstates of extremal black holes [22{24]. Given the lack, until recently,
of a good candidate for the holographic dual, the focus has been on attempts to describe
the e ects of the strong gravitational backreaction on AdS2 by nite energy excitations. As
elucidated recently by Almheiri and Polchinski [17] and further elaborated on in [20, 21],
to leading order the e ect of the gravitational backreaction can be described by a rather
universal AdS2 dilaton gravity model. In [19, 25, 26] it was argued that such a dilaton
gravity model provides a holographic description of the infrared limit of the
Sachdev-YeKitaev model [27, 28], a quantum mechanical system of Majorana fermions with random
long range interactions. Moreover, AdS2 dilaton gravity coupled to a gauge eld can also
provide a holographic description of the Kondo e ect [29].
In this paper we revisit the holographic dictionary and the asymptotic symmetries of
the speci c 2D Einstein-Maxwell-Dilaton (EMD) model
S2D =
with the aim to clarify certa (...truncated)