49 research outputs found
Symmetries, Horizons, and Black Hole Entropy
Black holes behave as thermodynamic systems, and a central task of any
quantum theory of gravity is to explain these thermal properties. A statistical
mechanical description of black hole entropy once seemed remote, but today we
suffer an embarrassment of riches: despite counting very different states, many
inequivalent approaches to quantum gravity obtain identical results. Such
``universality'' may reflect an underlying two-dimensional conformal symmetry
near the horizon, which can be powerful enough to control the thermal
characteristics independent of other details of the theory. This picture
suggests an elegant description of the relevant degrees of freedom as
Goldstone-boson-like excitations arising from symmetry breaking by the
conformal anomaly.Comment: 6 pages; first prize essay, 2007 Gravity Research Foundation essay
contes
Quantum field theory of metallic spin glasses
We introduce an effective field theory for the vicinity of a zero temperature
quantum transition between a metallic spin glass (``spin density glass'') and a
metallic quantum paramagnet. Following a mean field analysis, we perform a
perturbative renormalization-group study and find that the critical properties
are dominated by static disorder-induced fluctuations, and that dynamic
quantum-mechanical effects are dangerously irrelevant. A Gaussian fixed point
is stable for a finite range of couplings for spatial dimensionality ,
but disorder effects always lead to runaway flows to strong coupling for . Scaling hypotheses for a {\em static\/} strong-coupling critical field
theory are proposed. The non-linear susceptibility has an anomalously weak
singularity at such a critical point. Although motivated by a perturbative
study of metallic spin glasses, the scaling hypotheses are more general, and
could apply to other quantum spin glass to paramagnet transitions.Comment: 16 pages, REVTEX 3.0, 2 postscript figures; version contains
reference to related work in cond-mat/950412
From finite geometry exact quantities to (elliptic) scattering amplitudes for spin chains: the 1/2-XYZ
Initially, we derive a nonlinear integral equation for the vacuum counting
function of the spin 1/2-XYZ chain in the {\it disordered regime}, thus
paralleling similar results by Kl\"umper \cite{KLU}, achieved through a
different technique in the {\it antiferroelectric regime}. In terms of the
counting function we obtain the usual physical quantities, like the energy and
the transfer matrix (eigenvalues). Then, we introduce a double scaling limit
which appears to describe the sine-Gordon theory on cylindrical geometry, so
generalising famous results in the plane by Luther \cite{LUT} and Johnson et
al. \cite{JKM}. Furthermore, after extending the nonlinear integral equation to
excitations, we derive scattering amplitudes involving solitons/antisolitons
first, and bound states later. The latter case comes out as manifestly related
to the Deformed Virasoro Algebra of Shiraishi et al. \cite{SKAO}. Although this
nonlinear integral equations framework was contrived to deal with finite
geometries, we prove it to be effective for discovering or rediscovering
S-matrices. As a particular example, we prove that this unique model furnishes
explicitly two S-matrices, proposed respectively by Zamolodchikov \cite{ZAMe}
and Lukyanov-Mussardo-Penati \cite{LUK, MP} as plausible scattering description
of unknown integrable field theories.Comment: Article, 41 pages, Late
Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states
When the two-dimensional random-bond Ising model is represented as a
noninteracting fermion problem, it has the same symmetries as an ensemble of
random matrices known as class D. A nonlinear sigma model analysis of the
latter in two dimensions has previously led to the prediction of a metallic
phase, in which the fermion eigenstates at zero energy are extended. In this
paper we argue that such behavior cannot occur in the random-bond Ising model,
by showing that the Ising spin correlations in the metallic phase violate the
bound on such correlations that results from the reality of the Ising
couplings. Some types of disorder in spinless or spin-polarized p-wave
superconductors and paired fractional quantum Hall states allow a mapping onto
an Ising model with real but correlated bonds, and hence a metallic phase is
not possible there either. It is further argued that vortex disorder, which is
generic in the fractional quantum Hall applications, destroys the ordered or
weak-pairing phase, in which nonabelian statistics is obtained in the pure
case.Comment: 13 pages; largely independent of cond-mat/0007254; V. 2: as publishe
Survival-Time Distribution for Inelastic Collapse
In a recent publication [PRL {\bf 81}, 1142 (1998)] it was argued that a
randomly forced particle which collides inelastically with a boundary can
undergo inelastic collapse and come to rest in a finite time. Here we discuss
the survival probability for the inelastic collapse transition. It is found
that the collapse-time distribution behaves asymptotically as a power-law in
time, and that the exponent governing this decay is non-universal. An
approximate calculation of the collapse-time exponent confirms this behaviour
and shows how inelastic collapse can be viewed as a generalised persistence
phenomenon.Comment: 4 pages, RevTe
Liquid antiferromagnets in two dimensions
It is shown that, for proper symmetry of the parent lattice,
antiferromagnetic order can survive in two-dimensional liquid crystals and even
isotropic liquids of point-like particles, in contradiction to what common
sense might suggest. We discuss the requirements for antiferromagnetic order in
the absence of translational and/or orientational lattice order. One example is
the honeycomb lattice, which upon melting can form a liquid crystal with
quasi-long-range orientational and antiferromagnetic order but short-range
translational order. The critical properties of such systems are discussed.
Finally, we draw conjectures for the three-dimensional case.Comment: 4 pages RevTeX, 4 figures include
Open strings, 2D gravity and AdS/CFT correspondence
We present a detailed discussion of the duality between dilaton gravity on
AdS_2 and open strings. The correspondence between the two theories is
established using their symmetries and field theoretical, thermodynamic, and
statistical arguments. We use the dual conformal field theory to describe
two-dimensional black holes. In particular, all the semiclassical features of
the black holes, including the entropy, have a natural interpretation in terms
of the dual microscopic conformal dynamics. The previous results are discussed
in the general framework of the Anti-de Sitter/Conformal Field Theory
dualities.Comment: 22 pages, Typeset using REVTE
Boundary Liouville theory at c=1
The c=1 Liouville theory has received some attention recently as the
Euclidean version of an exact rolling tachyon background. In an earlier paper
it was shown that the bulk theory can be identified with the interacting c=1
limit of unitary minimal models. Here we extend the analysis of the c=1-limit
to the boundary problem. Most importantly, we show that the FZZT branes of
Liouville theory give rise to a new 1-parameter family of boundary theories at
c=1. These models share many features with the boundary Sine-Gordon theory, in
particular they possess an open string spectrum with band-gaps of finite width.
We propose explicit formulas for the boundary 2-point function and for the
bulk-boundary operator product expansion in the c=1 boundary Liouville model.
As a by-product of our analysis we also provide a nice geometric interpretation
for ZZ branes and their relation with FZZT branes in the c=1 theory.Comment: 37 pages, 1 figure. Minor error corrected, slight change in result
(1.6
On the energy-momentum tensor for a scalar field on manifolds with boundaries
We argue that already at classical level the energy-momentum tensor for a
scalar field on manifolds with boundaries in addition to the bulk part contains
a contribution located on the boundary. Using the standard variational
procedure for the action with the boundary term, the expression for the surface
energy-momentum tensor is derived for arbitrary bulk and boundary geometries.
Integral conservation laws are investigated. The corresponding conserved
charges are constructed and their relation to the proper densities is
discussed. Further we study the vacuum expectation value of the energy-momentum
tensor in the corresponding quantum field theory. It is shown that the surface
term in the energy-momentum tensor is essential to obtain the equality between
the vacuum energy, evaluated as the sum of the zero-point energies for each
normal mode of frequency, and the energy derived by the integration of the
corresponding vacuum energy density. As an application, by using the zeta
function technique, we evaluate the surface energy for a quantum scalar field
confined inside a spherical shell.Comment: 25 pages, 2 figures, section and appendix on the surface energy for a
spherical shell are added, references added, accepted for publication in
Phys. Rev.