22,928 research outputs found
Mass in anti-de Sitter spaces
The boundary stress tensor approach has proven extremely useful in defining
mass and angular momentum in asymptotically anti-de Sitter spaces with CFT
duals. An integral part of this method is the use of boundary counterterms to
regulate the gravitational action and stress tensor. In addition to the
standard gravitational counterterms, in the presence of matter we advocate the
use of a finite counterterm proportional to phi^2 (in five dimensions). We
demonstrate that this finite shift is necessary to properly reproduce the
expected mass/charge relation for R-charged black holes in AdS_5.Comment: 15 pages, late
Four dimensional Lie symmetry algebras and fourth order ordinary differential equations
Realizations of four dimensional Lie algebras as vector fields in the plane
are explicitly constructed. Fourth order ordinary differential equations which
admit such Lie symmetry algebras are derived. The route to their integration is
described.Comment: 12 page
A comment on discrete Kalb-Ramond field on orientifold and rank reduction
We show that the rank reduction of the gauge group on orientifolds in
presence of non vanishing discrete Kalb-Ramond field can be explained by the
presence of an induced field strength in a non trivial bundle on the branes.
This field strength is also necessary for the tadpole cancellation and the
number of branes is left unchanged by the presence of the discrete Kalb-Ramond
background.Comment: v2: added references, improved introduction and corrected misprints;
15 page
A perturbative re-analysis of N=4 supersymmetric Yang--Mills theory
The finiteness properties of the N=4 supersymmetric Yang-Mills theory are
reanalyzed both in the component formulation and using N=1 superfields, in
order to discuss some subtleties that emerge in the computation of gauge
dependent quantities. The one-loop corrections to various Green functions of
elementary fields are calculated. In the component formulation it is shown that
the choice of the Wess-Zumino gauge, that is standard in supersymmetric gauge
theories, introduces ultraviolet divergences in the propagators at the one-loop
level. Such divergences are exactly cancelled when the contributions of the
fields that are put to zero in the Wess-Zumino gauge are taken into account. In
the description in terms of N=1 superfields infrared divergences are found for
every choice of gauge different from the supersymmetric generalization of the
Fermi-Feynman gauge. Two-, three- and four-point functions of N=1 superfields
are computed and some general features of the infrared problem are discussed.
We also examine the effect of the introduction of mass terms for the (anti)
chiral superfields in the theory, which break supersymmetry from N=4 to N=1. It
is shown that in the mass deformed model no ultraviolet divergences appear in
two-point functions. It argued that this result can be generalized to n-point
functions, supporting the proposal of a possible of use of this modified model
as a supersymmetry-preserving regularization scheme for N=1 theories.Comment: 41 pages, LaTeX2e, uses feynMP package to draw Feynman diagram
A Curious Truncation of N=4 Yang-Mills
The coupling constant dependence of correlation functions of BPS operators in
N=4 Yang-Mills can be expressed in terms of integrated correlation functions.
We approximate these integrated correlators by using a truncated OPE expansion.
This leads to differential equations for the coupling dependence. When applied
to a particular sixteen point correlator, the coupling dependence we find
agrees with the corresponding amplitude computed via the AdS/CFT
correspondence. We conjecture that this truncation becomes exact in the large N
and large 't Hooft coupling limit.Comment: 10 pages, LaTeX; additional comments, added reference
Regret Bounds for Reinforcement Learning with Policy Advice
In some reinforcement learning problems an agent may be provided with a set
of input policies, perhaps learned from prior experience or provided by
advisors. We present a reinforcement learning with policy advice (RLPA)
algorithm which leverages this input set and learns to use the best policy in
the set for the reinforcement learning task at hand. We prove that RLPA has a
sub-linear regret of \tilde O(\sqrt{T}) relative to the best input policy, and
that both this regret and its computational complexity are independent of the
size of the state and action space. Our empirical simulations support our
theoretical analysis. This suggests RLPA may offer significant advantages in
large domains where some prior good policies are provided
Integrability of anisotropic and homogeneous Universes in scalar-tensor theory of gravitation
In this paper, we develop a method based on the analysis of the Kovalewski
exponents to study the integrability of anisotropic and homogeneous Universes.
The formalism is developed in scalar-tensor gravity, the general relativistic
case appearing as a special case of this larger framework. Then, depending on
the rationality of the Kovalewski exponents, the different models, both in the
vacuum and in presence of a barotropic matter fluid, are classified, and their
integrability is discussed.Comment: 16 pages, no figure, accepted in CQ
Simple model for quantum general relativity from loop quantum gravity
New progress in loop gravity has lead to a simple model of `general-covariant
quantum field theory'. I sum up the definition of the model in self-contained
form, in terms accessible to those outside the subfield. I emphasize its
formulation as a generalized topological quantum field theory with an infinite
number of degrees of freedom, and its relation to lattice theory. I list the
indications supporting the conjecture that the model is related to general
relativity and UV finite.Comment: 8 pages, 3 figure
Explicit Construction of Yang-Mills Instantons on ALE Spaces
We describe the explicit construction of Yang-Mills instantons on ALE spaces,
following the work of Kronheimer and Nakajima. For multicenter ALE metrics, we
determine the abelian instanton connections which are needed for the
construction in the non-abelian case. We compute the partition function of
Maxwell theories on ALE manifolds and comment on the issue of electromagnetic
duality. We discuss the topological characterization of the instanton bundles
as well as the identification of their moduli spaces. We generalize the 't
Hooft ansatz to SU(2) instantons on ALE spaces and on other hyper-Kahler
manifolds. Specializing to the Eguchi-Hanson gravitational background, we
explicitly solve the ADHM equations for SU(2) gauge bundles with second Chern
class 1/2, 1 and 3/2.Comment: 59 pages, epsf.tex, 2 figures included, uuencoded fil
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