AdS _{2} holographic dictionary
Here, we construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional EinsteinMaxwellDilaton theory that is obtained by a circle reduction from EinsteinHilbert 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 nonmore »
 Authors:

^{[1]};
^{[2]}
 Univ. of Pennsylvania, Philadelphia, PA (United States); Univ. of Maribor, Maribor (Slovenia)
 SISSA and INFN  Sezione di Trieste, Trieste (Italy)
 Publication Date:
 Grant/Contract Number:
 SC0013528
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 12; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Univ. of Pennsylvania, Philadelphia, PA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 2D gravity; AdSCFT correspondence; black holes; spacetime symmetries
 OSTI Identifier:
 1363954
Cvetic, Mirjam, and Papadimitriou, Ioannis. AdS2 holographic dictionary. United States: N. p.,
Web. doi:10.1007/JHEP12(2016)008.
Cvetic, Mirjam, & Papadimitriou, Ioannis. AdS2 holographic dictionary. United States. doi:10.1007/JHEP12(2016)008.
Cvetic, Mirjam, and Papadimitriou, Ioannis. 2016.
"AdS2 holographic dictionary". United States.
doi:10.1007/JHEP12(2016)008. https://www.osti.gov/servlets/purl/1363954.
@article{osti_1363954,
title = {AdS2 holographic dictionary},
author = {Cvetic, Mirjam and Papadimitriou, Ioannis},
abstractNote = {Here, we construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional EinsteinMaxwellDilaton theory that is obtained by a circle reduction from EinsteinHilbert 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, in agreement with the results of Castro and Song. Finally, we demonstrate that any solution of this specific dilaton gravity model can be uplifted to a family of asymptotically AdS2 × S2 or conformally AdS2 × S2 solutions of the STU model in four dimensions, including non extremal black holes. As a result, 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.},
doi = {10.1007/JHEP12(2016)008},
journal = {Journal of High Energy Physics (Online)},
number = 12,
volume = 2016,
place = {United States},
year = {2016},
month = {12}
}