On the stress tensor of Kerr/CFT

Abstract

The recently-conjectured Kerr/CFT correspondence posits a field theory dual to dynamics in the near-horizon region of an extreme Kerr black hole with certain boundary conditions. We construct a boundary stress tensor for this theory via covariant phase space techniques. The structure of the stress tensor indicates that any dual theory is a discrete light cone quantum theory, in agreement with recent arguments by Balasubramanian et al. The key technical step in our construction is the addition of an appropriate counter-term to the symplectic structure, which is necessary to make the theory fully covariant and to resolve a subtle problem involving the integrability of charges.

Note on Kerr/CFT correspondence in a first order formalism

“…This subtle issue is apparently overlooked in the existing calculations of Poisson brackets of charges in the second order formulation. This has already been pointed out in [3] for instance.…”

“…Therefore, the symplectic structure given in [7] may not be hypersurface independent for the boundary conditions appropriate for the NHEK geometry. This has been pointed out for Kerr/CFT in [3].…”

Near horizon extremal geometry perturbations: dynamical field perturbations vs. parametric variations

“…Before closing this section we also comment that, as is known from the canonical formulation of general relativity, δE a are generators of asymptotic gauge transformation x → x+ξ a through the Poisson bracket, under the assumption of integrability, conservation and finiteness of charges [19]. If one assumes that a symplectic current exists such that these assumptions are satisfied, then:…”

“…and the corresponding field equations becomeD 2 − µ 2 R(r) = 0 , (C.9) O (s) Y λ,m i (θ) = λY λ,m i (θ) , (C.10) where D µ = ∇ µ − iqA µ , µ ∈ {t, r} µ 2 = λ + q 2 , q = k i m i − is , (C.11)and s is the spin of perturbations (−2 for gravitational perturbations and −1 for Maxwell perturbations). The solutions to (C.9) are hypergeometric functions[2,19]. The value of λ is constrained by the equation on compact space H. The regularity of solutions at poles restricts the eigenvalues λ to discrete values with a lower bound depending on the field spin.…”

Hidden conformal symmetry of extremal Kerr-Bolt spacetimes

“…For the other works done on Kerr /CFT correspondence see . Subsequently, the Kerr/CFT correspondence was extended to the case of near-extremal black holes [37] (see also [38][39][40][41]). The main progresses are made essentially on the extremal and near extremal limits in which the black hole near horizon geometries consist a certain AdS structure and the central charges of dual CFT can be obtained by analyzing the asymptotic symmetry following the method in [42] or by calculating the boundary stress tensor of the 2D effective action [43].…”