226 research outputs found
Cardy and Kerr
The Kerr/CFT correspondence employs the Cardy formula to compute the entropy
of the left moving CFT states. This computation, which correctly reproduces the
Bekenstein--Hawking entropy of the four-dimensional extremal Kerr black hole,
is performed in a regime where the temperature is of order unity rather than in
a high-temperature regime. We show that the comparison of the entropy of the
extreme Kerr black hole and the entropy in the CFT can be understood within the
Cardy regime by considering a D0-D6 system with the same entropic properties.Comment: 20 pages; LaTeX; JHEP format; v.2 references added, v.3 Section 4
adde
Kerr-CFT From Black-Hole Thermodynamics
We analyze the near-horizon limit of a general black hole with two commuting
killing vector fields in the limit of zero temperature. We use black hole
thermodynamics methods to relate asymptotic charges of the complete spacetime
to those obtained in the near-horizon limit. We then show that some
diffeomorphisms do alter asymptotic charges of the full spacetime, even though
they are defined in the near horizon limit and, therefore, count black hole
states. We show that these conditions are essentially the same as considered in
the Kerr/CFT corresponcence. From the algebra constructed from these
diffeomorphisms, one can extract its central charge and then obtain the black
hole entropy by use of Cardy's formula.Comment: 19 pages, JHEP3, no figures. V2: References added, small typos fixe
Scattering and duality in the 2 dimensional OSP(2|2) Gross Neveu and sigma models
We write the thermodynamic Bethe ansatz for the massive OSp(2|2) Gross Neveu
and sigma models. We find evidence that the GN S matrix proposed by Bassi and
Leclair [12] is the correct one. We determine features of the sigma model S
matrix, which seem highly unconventional; we conjecture in particular a
relation between this sigma model and the complex sine-Gordon model at a
particular value of the coupling. We uncover an intriguing duality between the
OSp(2|2) GN (resp. sigma) model on the one hand, and the SO(4) sigma (resp. GN
model) on the other, somewhat generalizing to the massive case recent results
on OSp(4|2). Finally, we write the TBA for the (SUSY version of the) flow into
the random bond Ising model proposed by Cabra et al. [39], and conclude that
their S matrix cannot be correct.Comment: 41 pages, 27 figures. v2: minor revisio
Beyond Logarithmic Corrections to Cardy Formula
As shown by Cardy modular invariance of the partition function of a given
unitary non-singular 2d CFT with left and right central charges c_L and c_R,
implies that the density of states in a microcanonical ensemble, at excitations
Delta and Delta-bar and in the saddle point approximation, is
\rho_0(\Delta,\bar\Delta;c_L, c_R)=c_L c_R
\exp(2\pi\sqrt{{c_L\Delta}/{6}})\exp(2\pi\sqrt{{c_R\bar\Delta}/{6}}). In this
paper, we extend Cardy's analysis and show that in the saddle point
approximation and up to contributions which are exponentially suppressed
compared to the leading Cardy's result, the density of states takes the form
\rho(\Delta,\bar\Delta; c_L,c_R)= f(c_L\Delta)
f(c_R\bar\Delta)\rho_0(\Delta,\bar\Delta; c_L, c_R), for a function f(x) which
we specify. In particular, we show that (i) \rho (\Delta,\bar\Delta; c_L, c_R)
is the product of contributions of left and right movers and hence, to this
approximation, the partition function of any modular invariant, non-singular
unitary 2d CFT is holomorphically factorizable and (ii) \rho(\Delta,\bar\Delta;
c_L, c_R)/(c_Lc_R) is only a function of and . In
addition, treating \rho(\Delta,\bar\Delta; c_L, c_R) as the density of states
of a microcanonical ensemble, we compute the entropy of the system in the
canonical counterpart and show that the function f(x) is such that the
canonical entropy, up to exponentially suppressed contributions, is simply
given by the Cardy's result \ln\rho_0(\Delta,\bar\Delta; c_L, c_R).Comment: 30 pages, no figures; v2: minor improvements, one reference added,
v3: minor corrections to match the published versio
Field theories with anisotropic scaling in 2D, solitons and the microscopic entropy of asymptotically Lifshitz black holes
Field theories with anisotropic scaling in 1+1 dimensions are considered. It
is shown that the isomorphism between Lifshitz algebras with dynamical
exponents z and 1/z naturally leads to a duality between low and high
temperature regimes. Assuming the existence of gap in the spectrum, this
duality allows to obtain a precise formula for the asymptotic growth of the
number of states with a fixed energy which depends on z and the energy of the
ground state, and reduces to the Cardy formula for z=1. The holographic
realization of the duality can be naturally inferred from the fact that
Euclidean Lifshitz spaces in three dimensions with dynamical exponents and
characteristic lengths given by z, l, and 1/z, l/z, respectively, are
diffeomorphic. The semiclassical entropy of black holes with Lifshitz
asymptotics can then be recovered from the generalization of Cardy formula,
where the ground state corresponds to a soliton. An explicit example is
provided by the existence of a purely gravitational soliton solution for BHT
massive gravity, which precisely has the required energy that reproduces the
entropy of the analytic asymptotically Lifshitz black hole with z=3.
Remarkably, neither the asymptotic symmetries nor central charges were
explicitly used in order to obtain these results.Comment: 17 pages, no figures, references corrected and update
A de Sitter Hoedown
Rotating black holes in de Sitter space are known to have interesting limits
where the temperatures of the black hole and cosmological horizon are equal. We
give a complete description of the thermal phase structure of all allowed
rotating black hole configurations. Only one configuration, the rotating Nariai
limit, has the black hole and cosmological horizons both in thermal and
rotational equilibrium, in that both the temperatures and angular velocities of
the two horizons coincide. The thermal evolution of the spacetime is shown to
lead to the pure de Sitter spacetime, which is the most entropic configuration.
We then provide a comprehensive study of the wave equation for a massless
scalar in the rotating Nariai geometry. The absorption cross section at the
black hole horizon is computed and a condition is found for when the scattering
becomes superradiant. The boundary-to-boundary correlators at finite
temperature are computed at future infinity. The quasinormal modes are obtained
in explicit form. Finally, we obtain an expression for the expectation value of
the number of particles produced at future infinity starting from a vacuum
state with no incoming particles at past infinity. Some of our results are used
to provide further evidence for a recent holographic proposal between the
rotating Nariai geometry and a two-dimensional conformal field theory.Comment: 35 + 1 pages, 9 figures; v3: typos correcte
Kerr/CFT, dipole theories and nonrelativistic CFTs
We study solutions of type IIB supergravity which are SL(2,R) x SU(2) x
U(1)^2 invariant deformations of AdS_3 x S^3 x K3 and take the form of products
of self-dual spacelike warped AdS_3 and a deformed three-sphere. One of these
backgrounds has been recently argued to be relevant for a derivation of
Kerr/CFT from string theory, whereas the remaining ones are holographic duals
of two-dimensional dipole theories and their S-duals. We show that each of
these backgrounds is holographically dual to a deformation of the DLCQ of the
D1-D5 CFT by a specific supersymmetric (1,2) operator, which we write down
explicitly in terms of twist operators at the free orbifold point. The
deforming operator is argued to be exactly marginal with respect to the
zero-dimensional nonrelativistic conformal (or Schroedinger) group - which is
simply SL(2,R)_L x U(1)_R. Moreover, in the supergravity limit of large N and
strong coupling, no other single-trace operators are turned on. We thus propose
that the field theory duals to the backgrounds of interest are nonrelativistic
CFTs defined by adding the single Schroedinger-invariant (1,2) operator
mentioned above to the original CFT action. Our analysis indicates that the
rotating extremal black holes we study are best thought of as finite
right-moving temperature (non-supersymmetric) states in the above-defined
supersymmetric nonrelativistic CFT and hints towards a more general connection
between Kerr/CFT and two-dimensional non-relativistic CFTs.Comment: 48+8 pages, 4 figures; minor corrections and references adde
The entropy of black holes: a primer
After recalling the definition of black holes, and reviewing their energetics
and their classical thermodynamics, one expounds the conjecture of Bekenstein,
attributing an entropy to black holes, and the calculation by Hawking of the
semi-classical radiation spectrum of a black hole, involving a thermal
(Planckian) factor. One then discusses the attempts to interpret the black-hole
entropy as the logarithm of the number of quantum micro-states of a macroscopic
black hole, with particular emphasis on results obtained within string theory.
After mentioning the (technically cleaner, but conceptually more intricate)
case of supersymmetric (BPS) black holes and the corresponding counting of the
degeneracy of Dirichlet-brane systems, one discusses in some detail the
``correspondence'' between massive string states and non-supersymmetric
Schwarzschild black holes.Comment: 51 pages, 4 figures, talk given at the "Poincare seminar" (Paris, 6
December 2003), to appear in Poincare Seminar 2003 (Birkhauser
Holography For a De Sitter-Esque Geometry
Warped dS arises as a solution to topologically massive gravity (TMG)
with positive cosmological constant and Chern-Simons coefficient
in the region . It is given by a real line fibration
over two-dimensional de Sitter space and is equivalent to the rotating Nariai
geometry at fixed polar angle. We study the thermodynamic and asymptotic
structure of a family of geometries with warped dS asymptotics.
Interestingly, these solutions have both a cosmological horizon and an internal
one, and their entropy is unbounded from above unlike black holes in regular de
Sitter space. The asymptotic symmetry group resides at future infinity and is
given by a semi-direct product of a Virasoro algebra and a current algebra. The
right moving central charge vanishes when . We discuss the
possible holographic interpretation of these de Sitter-esque spacetimes.Comment: 22 pages, 1 figure; v2: typos corrected, to match with published
versio
- …