75 research outputs found
Fermions and noncommutative emergent gravity II: Curved branes in extra dimensions
We study fermions coupled to Yang-Mills matrix models from the point of view
of emergent gravity. The matrix model Dirac operator provides an appropriate
coupling for fermions to the effective gravitational metric for general branes
with nontrivial embedding, albeit with a non-standard spin connection. This
generalizes previous results for 4-dimensional matrix models. Integrating out
the fermions in a nontrivial geometrical background induces indeed the
Einstein-Hilbert action of the effective metric, as well as additional terms
which couple the Poisson tensor to the Riemann tensor, and a dilaton-like term.Comment: 34 pages; minor change
Anomalous Breaking of Anisotropic Scaling Symmetry in the Quantum Lifshitz Model
In this note we investigate the anomalous breaking of anisotropic scaling
symmetry in a non-relativistic field theory with dynamical exponent z=2. On
general grounds, one can show that there exist two possible "central charges"
which characterize the breaking of scale invariance. Using heat kernel methods,
we compute these two central charges in the quantum Lifshitz model, a free
field theory which is second order in time and fourth order in spatial
derivatives. We find that one of the two central charges vanishes.
Interestingly, this is also true for strongly coupled non-relativistic field
theories with a geometric dual described by a metric and a massive vector
field.Comment: 26 pages; major revision (results were unaffected), published versio
Generalized quark-antiquark potential at weak and strong coupling
We study a two-parameter family of Wilson loop operators in N=4
supersymmetric Yang-Mills theory which interpolates smoothly between the 1/2
BPS line or circle and a pair of antiparallel lines. These observables capture
a natural generalization of the quark-antiquark potential. We calculate these
loops on the gauge theory side to second order in perturbation theory and in a
semiclassical expansion in string theory to one-loop order. The resulting
determinants are given in integral form and can be evaluated numerically for
general values of the parameters or analytically in a systematic expansion
around the 1/2 BPS configuration. We comment about the feasibility of deriving
all-loop results for these Wilson loops.Comment: 43 pages: 15 comprising the main text and 25 for detailed appendice
The rolling problem: overview and challenges
In the present paper we give a historical account -ranging from classical to
modern results- of the problem of rolling two Riemannian manifolds one on the
other, with the restrictions that they cannot instantaneously slip or spin one
with respect to the other. On the way we show how this problem has profited
from the development of intrinsic Riemannian geometry, from geometric control
theory and sub-Riemannian geometry. We also mention how other areas -such as
robotics and interpolation theory- have employed the rolling model.Comment: 20 page
Quantum gravitational contributions to quantum electrodynamics
Quantum electrodynamics describes the interactions of electrons and photons.
Electric charge (the gauge coupling constant) is energy dependent, and there is
a previous claim that charge is affected by gravity (described by general
relativity) with the implication that the charge is reduced at high energies.
But that claim has been very controversial with the situation inconclusive.
Here I report an analysis (free from earlier controversies) demonstrating that
that quantum gravity corrections to quantum electrodynamics have a quadratic
energy dependence that result in the reduction of the electric charge at high
energies, a result known as asymptotic freedom.Comment: To be published in Nature. 19 pages LaTeX, no figure
Chiral Modulations in Curved Space I: Formalism
The goal of this paper is to present a formalism that allows to handle
four-fermion effective theories at finite temperature and density in curved
space. The formalism is based on the use of the effective action and zeta
function regularization, supports the inclusion of inhomogeneous and
anisotropic phases. One of the key points of the method is the use of a
non-perturbative ansatz for the heat-kernel that returns the effective action
in partially resummed form, providing a way to go beyond the approximations
based on the Ginzburg-Landau expansion for the partition function. The
effective action for the case of ultra-static Riemannian spacetimes with
compact spatial section is discussed in general and a series representation,
valid when the chemical potential satisfies a certain constraint, is derived.
To see the formalism at work, we consider the case of static Einstein spaces at
zero chemical potential. Although in this case we expect inhomogeneous phases
to occur only as meta-stable states, the problem is complex enough and allows
to illustrate how to implement numerical studies of inhomogeneous phases in
curved space. Finally, we extend the formalism to include arbitrary chemical
potentials and obtain the analytical continuation of the effective action in
curved space.Comment: 22 pages, 3 figures; version to appear in JHE
Poincare isomorphism in K-theory on manifolds with edges
The aim of this paper is to construct the Poincare isomorphism in K-theory on
manifolds with edges. We show that the Poincare isomorphism can naturally be
constructed in the framework of noncommutative geometry. More precisely, to a
manifold with edges we assign a noncommutative algebra and construct an
isomorphism between the K-group of this algebra and the K-homology group of the
manifold with edges viewed as a compact topological space.Comment: 15 pages, no figure
Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions
Euclidean gravity method has been successful in computing logarithmic
corrections to extremal black hole entropy in terms of low energy data, and
gives results in perfect agreement with the microscopic results in string
theory. Motivated by this success we apply Euclidean gravity to compute
logarithmic corrections to the entropy of various non-extremal black holes in
different dimensions, taking special care of integration over the zero modes
and keeping track of the ensemble in which the computation is done. These
results provide strong constraint on any ultraviolet completion of the theory
if the latter is able to give an independent computation of the entropy of
non-extremal black holes from microscopic description. For Schwarzschild black
holes in four space-time dimensions the macroscopic result seems to disagree
with the existing result in loop quantum gravity.Comment: LaTeX, 40 pages; corrected small typos and added reference
On duality symmetry in perturbative quantum theory
Non-compact symmetries of extended 4d supergravities involve duality
rotations of vectors and thus are not manifest off-shell invariances in
standard "second-order" formulation. To study how such symmetries are realised
in the quantum theory we consider examples in 2 dimensions where vector-vector
duality is replaced by scalar-scalar one. Using a "doubled" formulation, where
fields and their momenta are treated on an equal footing and the duality
becomes a manifest symmetry of the action (at the expense of Lorentz symmetry),
we argue that the corresponding on-shell quantum effective action or S-matrix
are duality symmetric as well as Lorentz invariant. The simplest case of
discrete Z_2 duality corresponds to a symmetry of the S-matrix under flipping
the sign of the negative-chirality scalars in 2 dimensions or phase rotations
of chiral (definite-helicity) parts of vectors in 4 dimensions. We also briefly
discuss some 4d models and comment on implications of our analysis for extended
supergravities.Comment: 21 pages, Latex v2: comments and references added v3: references and
minor comments adde
Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in Einstein-Maxwell Theory
We compute the second Seely-DeWitt coefficient of the kinetic operator of the
metric and gauge fields in Einstein-Maxwell theory in an arbitrary background
field configuration. We then use this result to compute the logarithmic
correction to the entropy of an extremal Kerr-Newmann black hole.Comment: 12 page
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