States and boundary terms: subtleties of lorentzian AdS/CFT

Abstract

Abstract:We complete the project of specifying the Lorentzian AdS/CFT correspondence and its approximation by bulk semi-classical methods begun by earlier authors. At the end, the Lorentzian treatment is self-contained and requires no analytic continuation from the Euclidean. The new features involve a careful study of boundary terms associated with an initial time t − and a final time t + . These boundary terms are determined by a choice of quantum states. The main results in the semi-classical approximation are 1) The times t ± may be finite, and need only label Cauchy surfaces respectively to the past and future of the points at which one wishes to obtain CFT correlators. Subject to this condition on t ± , we provide a bulk computation of CFT correlators that is manifestly independent of t ± . 2) As a result of (1), all CFT correlators can be expressed in terms of a path integral over regions of spacetime outside of any black hole horizons.3) The details of the boundary terms at t ± serve to guarrantee that, at leading order in this approximation, any CFT one-point function is given by a simple boundary value of the classical bulk solution at null infinity, I. This work is dedicated to the memory of Bryce S. DeWitt. The remarks in this paper largely study the relation of the AdS/CFT dictionary to the Schwinger variational principle, which the author first learned from DeWitt as a Ph.D. student.

Real-Time Gauge/Gravity Duality

“…The aim of this work is to provide a concrete, first principles prescription that covers all n-point functions and is applicable for any QFT that has (an Asymptotically AdS) holographic dual. Previous work on this subject includes [3,4,5] and our results agree with these works when we restrict to their respective domains of validity.The basic Euclidean holographic dictionary identifies the boundary conditions φ (0) for the bulk fields Φ to sources of the dual boundary operators and the bulk partition function, which is a functional of these boundary fields, to the generating functional of connected npoint functions. The main new issue that arises in the Lorentzian context is that in the bulk, on top of specifying boundary conditions φ (0) , one also needs to specify initial and/or final conditions φ ± for all fields, and the bulk partition function is also a functional of these.…”

Quasinormal modes of black holes and black branes

“…For Minkowski space correlators, there are subtleties resolved in [98,302] (recent work on the Lorentzian AdS/CFT includes [411,304]). Ref.…”

Comparison between various notions of conserved charges in asymptotically AdS spacetimes

“…This can be seen in different ways, for example by combining eqs. (57,58) with the constraint equation. Another way is to notice that, by combining Einstein's equation and the contracted Bianchi-identities, we have 0…”