SciPost Phys. 10, 024 (2021) ·
published 1 February 2021

· pdf
We use the variational principle approach to derive the large $N$ holographic
dictionary for twodimensional $T\bar T$deformed CFTs, for both signs of the
deformation parameter. The resulting dual gravitational theory has mixed
boundary conditions for the nondynamical graviton; the boundary conditions for
matter fields are undeformed. When the matter fields are turned off and the
deformation parameter is negative, the mixed boundary conditions for the metric
at infinity can be reinterpreted onshell as Dirichlet boundary conditions at
finite bulk radius, in agreement with a previous proposal by McGough, Mezei and
Verlinde. The holographic stress tensor of the deformed CFT is fixed by the
variational principle, and in pure gravity it coincides with the BrownYork
stress tensor on the radial bulk slice with a particular cosmological constant
counterterm contribution. In presence of matter fields, the connection between
the mixed boundary conditions and the radial "bulk cutoff" is lost. Only the
former correctly reproduce the energy of the bulk configuration, as expected
from the fact that a universal formula for the deformed energy can only depend
on the universal asymptotics of the bulk solution, rather than the details of
its interior. The asymptotic symmetry group associated with the mixed boundary
conditions consists of two commuting copies of a statedependent Virasoro
algebra, with the same central extension as in the original CFT.
Iosif Bena, Pierre Heidmann, Ruben Monten, Nicholas P. Warner
SciPost Phys. 7, 063 (2019) ·
published 14 November 2019

· pdf
We develop a new hybrid WKB technique to compute boundarytoboundary scalar
Green functions in asymptoticallyAdS backgrounds in which the scalar wave
equation is separable and is explicitly solvable in the asymptotic region. We
apply this technique to a family of sixdimensional $\frac{1}{8}$BPS
asymptotically AdS$_3\,\times\,$S$^3$ horizonless geometries that have the same
charges and angular momenta as a D1D5P black hole with a large horizon area.
At large and intermediate distances, these geometries very closely approximate
the extremalBTZ$\,\times\,$S$^3$ geometry of the black hole, but instead of
having an event horizon, these geometries have a smooth highlyredshifted
globalAdS$_3\,\times\,$S$^3$ cap in the IR. We show that the response function
of a scalar probe, in momentum space, is essentially given by the pole
structure of the highlyredshifted globalAdS$_3$ modulated by the BTZ response
function. In position space, this translates into a sharp exponential
blackholelike decay for times shorter than $N_1 N_5$, followed by the
emergence of evenly spaced "echoes from the cap," with period $\sim N_1 N_5$.
Our result shows that horizonless microstate geometries can have the same
thermal decay as black holes without the associated information loss.
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