Journal of High Energy Physics

, 2017:203 | Cite as

Menagerie of AdS2 boundary conditions

  • Daniel GrumillerEmail author
  • Robert McNees
  • Jakob Salzer
  • Carlos Valcárcel
  • Dmitri Vassilevich
Open Access
Regular Article - Theoretical Physics


We consider different sets of AdS2 boundary conditions for the Jackiw-Teitelboim model in the linear dilaton sector where the dilaton is allowed to fluctuate to leading order at the boundary of the Poincaré disk. The most general set of boundary conditions is easily motivated in the gauge theoretic formulation as a Poisson sigma model and has an \( \mathfrak{s}\mathfrak{l}(2) \) current algebra as asymptotic symmetries. Consistency of the variational principle requires a novel boundary counterterm in the holographically renormalized action, namely a kinetic term for the dilaton. The on-shell action can be naturally reformulated as a Schwarzian boundary action. While there can be at most three canonical boundary charges on an equal-time slice, we consider all Fourier modes of these charges with respect to the Euclidean boundary time and study their associated algebras. Besides the (centerless) \( \mathfrak{s}\mathfrak{l}(2) \) current algebra we find for stricter boundary conditions a Virasoro algebra, a warped conformal algebra and a \( \mathfrak{u}(1) \) current algebra. In each of these cases we get one half of a corresponding symmetry algebra in three-dimensional Einstein gravity with negative cosmological constant and analogous boundary conditions. However, on-shell some of these algebras reduce to finite-dimensional ones, reminiscent of the on-shell breaking of conformal invariance in SYK. We conclude with a discussion of thermodynamical aspects, in particular the entropy and some Cardyology.


2D Gravity AdS-CFT Correspondence Topological Field Theories 


Open Access

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Authors and Affiliations

  1. 1.Institute for Theoretical Physics, TU WienViennaAustria
  2. 2.Department of PhysicsLoyola University ChicagoChicagoU.S.A.
  3. 3.CMCC-Universidade Federal do ABCSanto AndréBrazil
  4. 4.Department of PhysicsTomsk State UniversityTomskRussia

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