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Non-AdS holography in 3-dimensional higher spin gravity - General recipe and example

H. Afshar, M. Gary, D. Grumiller, R. Rashkov, M. Riegler

Abstract

We present the general algorithm to establish the classical and quantum asymptotic symmetry algebra for non-AdS higher spin gravity and implement it for the specific example of spin-3 gravity in the non-principal embedding with Lobachevsky (H^2xR) boundary conditions. The asymptotic symmetry algebra for this example consists of a quantum W_3^2 (Polyakov-Bershadsky) and an affine u(1) algebra. We show that unitary representations of the quantum W_3^2 algebra exist only for two values of its central charge, the trivial c=0 "theory" and the simple c=1 theory.

Non-AdS holography in 3-dimensional higher spin gravity - General recipe and example

Abstract

We present the general algorithm to establish the classical and quantum asymptotic symmetry algebra for non-AdS higher spin gravity and implement it for the specific example of spin-3 gravity in the non-principal embedding with Lobachevsky (H^2xR) boundary conditions. The asymptotic symmetry algebra for this example consists of a quantum W_3^2 (Polyakov-Bershadsky) and an affine u(1) algebra. We show that unitary representations of the quantum W_3^2 algebra exist only for two values of its central charge, the trivial c=0 "theory" and the simple c=1 theory.

Paper Structure

This paper contains 19 sections, 60 equations.

Table of Contents

  1. Introduction
  2. General algorithm for non-AdS higher spin holography
  3. 1.
  4. 2.
  5. 3.
  6. 4.
  7. 5.
  8. 6.
  9. 7.
  10. Background and boundary conditions
  11. Canonical analysis and asymptotic symmetry algebra
  12. Quantum asymptotic symmetry algebra
  13. Unitary representations and possible field theory duals
  14. $\hat{k}=-\frac{3}{2}$ and $\hat{c}=0$
  15. $\hat{k}=-1$ and $\hat{c}=1$
  16. ...and 4 more sections