AdS2 holographic dictionary

Abstract

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 specific model ensures that the dual theory has a well defined ultraviolet completion in terms of a two dimensional conformal field 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 find 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. We further show that the only 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 Compère, Song and Strominger [1], in agreement with the results of Castro and Song [2]. Finally, we demonstrate that any solution of this specific dilaton gravity model can be uplifted to a family of asymptotically AdS 2 × S 2 or conformally AdS 2 × S 2 solutions of the STU model 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.

Supersymmetric SYK model and random matrix theory

“…SYK model [6][7][8][9][10] is a microscopic quantum hamiltonian with random Gaussian non-local couplings among majonara fermions. As is maximally chaotic and nearly conformal, this model could be treated as a holographic dual of quantum black hole with AdS 2 horizon through the (near) AdS/CFT correspondence [11][12][13][14][15][16][17][18][19][20]. In the recent research people have also discussed several generalizations of the SYK model [21][22][23][24], such as higher dimensional generalizations and supersymmetric constraints.…”

Deformations of the Almheiri-Polchinski model

“…Another counter-term may be allowed and it would be nice to seek for it by following the procedure in [78]. We are grateful to Ioannis Papadimitriou for this point.…”

Erratum to: AdS2 holographic dictionary

“…1 Like the one-point functions in eq. (3.14) of [1], (2) is exact in the sources α(t), β(t) and µ(t), although the fact that S global has not been determined allows us to add an arbitrary total derivative term in this expression. In particular, successively differentiating (2) or the onepoint functions in eq.…”

“…In particular, successively differentiating (2) or the onepoint functions in eq. (3.14) of [1] with respect to the sources α(t), β(t) and µ(t) one can evaluate any n-point correlation function of the operators T , O ψ and J t in the dual theory.…”