Boundary conditions for warped AdS3 in quadratic ensemble
Ankit Aggarwal (Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, 1098 XH, The Netherlands, Physique Mathématique des Interactions Fondamentales & International Solvay Institutes, Université Libre de Bruxelles, Campus Plaine — CP 231, Bruxelles, 1050, Belgium); Luca Ciambelli (Physique Mathématique des Interactions Fondamentales & International Solvay Institutes, Université Libre de Bruxelles, Campus Plaine — CP 231, Bruxelles, 1050, Belgium); Stéphane Detournay (Physique Mathématique des Interactions Fondamentales & International Solvay Institutes, Université Libre de Bruxelles, Campus Plaine — CP 231, Bruxelles, 1050, Belgium); Antoine Somerhausen (Physique Mathématique des Interactions Fondamentales & International Solvay Institutes, Université Libre de Bruxelles, Campus Plaine — CP 231, Bruxelles, 1050, Belgium)
In the context of warped conformal field theories (WCFT), the derivation of the warped Cardy formula relies on the zero mode spectrum being bounded from below. Generically, this is not true for holographic WCFTs in “canonical” ensemble, whereas this condition is satisfied in the “quadratic” ensemble, making it more natural in holographic setups. In this work, we find a new set of boundary conditions in three-dimensional Topologically Massive Gravity (TMG) such that the putative dual theory is a WCFT in quadratic ensemble. Surprisingly, imposing the equations of motion, we obtain a closed form metric spanned by two arbitrary chiral functions, analogous to the Bañados metrics in Einstein gravity. Surface charges for these boundary conditions are not a priori integrable and we discuss two choices of boundary conditions to make them so. We obtain the bulk thermodynamic entropy of warped BTZ black holes by making use of the warped Cardy formula, in its regime of validity. We also discuss the issue of identifying the vacuum in our solution space: demanding the enhancement of global symmetries selects only a family of solutions, out of which the unique vacuum must be carefully singled out.
