SciPost Phys. 8, 010 (2020) ·
published 23 January 2020

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We perform the Hamiltonian reduction of three dimensional Einstein gravity
with negative cosmological constant under constraints imposed by near horizon
boundary conditions. The theory reduces to a FloreaniniJackiw type scalar
field theory on the horizon, where the scalar zero modes capture the global
black hole charges. The near horizon Hamiltonian is a total derivative term,
which explains the softness of all oscillator modes of the scalar field. We
find also a (Kortewegde Vries) hierarchy of modified boundary conditions that
we use to lift the degeneracy of the soft hair excitations on the horizon.
Christian Ecker, Daniel Grumiller, Wilke van der Schee, Shahin SheikhJabbari, Philipp Stanzer
SciPost Phys. 6, 036 (2019) ·
published 25 March 2019

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We consider the Quantum Null Energy Condition (QNEC) for holographic
conformal field theories in two spacetime dimensions (CFT$_2$). We show that
QNEC saturates for all states dual to vacuum solutions of AdS$_3$ Einstein
gravity, including systems that are far from thermal equilibrium. If the
RyuTakayanagi surface encounters bulk matter QNEC does not need to be
saturated, whereby we give both analytical and numerical examples. In
particular, for CFT$_2$ with a global quench dual to AdS$_3$Vaidya geometries
we find a curious halfsaturation of QNEC for large entangling regions. We also
address order one corrections from quantum backreactions of a scalar field in
AdS$_3$ dual to a primary operator of dimension $h$ in a large central charge
expansion and explicitly compute both, the backreacted RyuTakayanagi surface
part and the bulk entanglement contribution to EE and QNEC. At leading order
for small entangling regions the contribution from bulk EE exactly cancels the
contribution from the backreacted RyuTakayanagi surface, but at higher orders
in the size of the region the contributions are almost equal while QNEC is not
saturated. For a halfspace entangling region we find that QNEC is gapped by
$h/4$ in the large $h$ expansion.
Prof. Grumiller: "** Response to referee 1 ** ..."
in Report on Near horizon dynamics of three dimensional black holes