Dionysios Anninos, Diego M. Hofman, Jorrit Kruthoff
SciPost Phys. 7, 054 (2019) ·
published 23 October 2019

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We consider quantum field theory near the horizon of an extreme Kerr black
hole. In this limit, the dynamics is well approximated by a tower of
electrically charged fields propagating in an $SL(2,\mathbb{R})$ invariant
AdS$_2$ geometry endowed with a constant, symmetry preserving background
electric field. At large charge the fields oscillate near the AdS$_2$ boundary
and no longer admit a standard Dirichlet treatment. From the Kerr black hole
perspective, this phenomenon is related to the presence of an ergosphere. We
discuss a definition for the quantum field theory whereby we 'UV' complete
AdS$_2$ by appending an asymptotically two dimensional Minkowski region. This
allows the construction of a novel observable for the fluxcarrying modes that
resembles the standard flat space Smatrix. We relate various features
displayed by the highly charged particles to the principal series
representations of $SL(2,\mathbb{R})$. These representations are unitary and
also appear for massive quantum fields in dS$_2$. Both fermionic and bosonic
fields are studied. We find that the free charged massless fermion is exactly
solvable for general background, providing an interesting arena for the problem
at hand.
SciPost Phys. 5, 060 (2018) ·
published 10 December 2018

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We investigate the existence of a stateoperator correspondence on the torus.
This correspondence would relate states of the CFT Hilbert space living on a
spatial torus to the path integral over compact Euclidean manifolds with
operator insertions. Unlike the states on the sphere that are associated to
local operators, we argue that those on the torus would more naturally be
associated to line operators. We find evidence that such a correspondence
cannot exist and in particular, we argue that no compact Euclidean path
integral can produce the vacuum on the torus. Our arguments come solely from
field theory and formulate a CFT version of the HorowitzMyers conjecture for
the AdS soliton.
Submissions
Submissions for which this Contributor is identified as an author:
Mr Kruthoff: "Please note the following typo..."
in Submission on Comments on a stateoperator correspondence for the torus by Alexandre Belin, Jan de Boer, Jorrit Kruthoff