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Clearing the Throat Irrelevant Operators and Finite Temperature in Large n Gauge Theory
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Clearing the Throat:
Irrelevant Operators and Finite Temperature
in Large N Gauge Theory
Nick Evans?, Clifford V. Johnson?, Michela Petrini?
?Department of Physics, University of Southampton
Southampton SO17 1BJ, U.K.
n.evans@hep.phys.soton.ac.uk
?Centre for Particle Theory, Department of Mathematical Sciences
University of Durham, Durham, DH1 3LE, U.K.
c.v.johnson@durham.ac.uk
?Centre de Physique The?orique, Ecole Polytechnique
F-91128 Palaiseau cedex, France
michela.petrini@cpht.polytechnique.fr
Abstract
We study the addition of an irrelevant operator to the N = 4 supersymmetric large N
SU(N) gauge theory, in the presence of finite temperature, T . In the supergravity dual,
the effect of the operator is known to correspond to a deformation of the AdS5 × S5
“throat” which restores the asymptotic ten dimensional Minkowski region of spacetime,
completing the full D3–brane solution. The system at non–zero T is interesting, since at
the extremes of some of the geometrical parameters the geometry interpolates between
a seven dimensional spherical Minkowskian Schwarzschild black hole (times R3) and a
five dimensional flat AdS Schwarzschild black hole (times S5). We observe that when the
coupling of the operator reaches a critical value, the deconfined phase, which is represented
by the geometry with horizon, disappears for all temperatures, returning the system to a
confined phase which is represented by the thermalised extremal geometry.
1
1 Introduction
A number of important spacetime solutions of general relativity and string theory have the
interesting feature that they have an infinite “throat” spacetime at their core, connected to
the asymptotically flat region by an interpolating region or “mouth”. A simple prototype of
this is the extremal Reissner–Nordstrom black hole in four dimensions, at whose core there is
AdS2 × S2, the Bertotti–Robinson universe[1]. This behaviour persists to various spacet
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