11,143 research outputs found
Higher Spin AdS/CFT at One Loop
Following arXiv:1308.2337, we carry out one loop tests of higher spin
AdS/CFT correspondences for . The Vasiliev theories in
AdS, which contain each integer spin once, are related to the
singlet sector of the -dimensional CFT of free complex scalar fields;
the minimal theories containing each even spin once -- to the singlet
sector of the CFT of free real scalar fields. Using analytic continuation
of higher spin zeta functions, which naturally regulate the spin sums, we
calculate one loop vacuum energies in Euclidean AdS. In even we
compare the result with the correction to the -coefficient of the
Weyl anomaly; in odd -- with the correction to the free energy
on the -dimensional sphere. For the theories of integer spins, the
correction vanishes in agreement with the CFT of free complex scalars. For
the minimal theories, the correction always equals the contribution of one real
conformal scalar field in dimensions. As explained in arXiv:1308.2337, this
result may agree with the singlet sector of the theory of real
scalar fields, provided the coupling constant in the higher spin theory is
identified as . Our calculations in even are closely
related to finding the regularized -anomalies of conformal higher spin
theories. In each even we identify two such theories with vanishing
-anomaly: a theory of all integer spins, and a theory of all even spins
coupled to a complex conformal scalar. We also discuss an interacting UV fixed
point in obtained from the free scalar theory via an irrelevant
double-trace quartic interaction. This interacting large theory is dual to
the Vasiliev theory in AdS where the bulk scalar is quantized with the
alternate boundary condition.Comment: 35 pages. v2: minor improvement
The Infrastructure of a Global Field of Arbitrary Unit Rank
In this paper, we show a general way to interpret the infrastructure of a
global field of arbitrary unit rank. This interpretation generalizes the prior
concepts of the giant step operation and f-representations, and makes it
possible to relate the infrastructure to the (Arakelov) divisor class group of
the global field. In the case of global function fields, we present results
that establish that effective implementation of the presented methods is indeed
possible, and we show how Shanks' baby-step giant-step method can be
generalized to this situation.Comment: Revised version. Accepted for publication in Math. Com
Analytic continuation of functional renormalization group equations
Functional renormalization group equations are analytically continued from
imaginary Matsubara frequencies to the real frequency axis. On the example of a
scalar field with O(N) symmetry we discuss the analytic structure of the
flowing action and show how it is possible to derive and solve flow equations
for real-time properties such as propagator residues and particle decay widths.
The formalism conserves space-time symmetries such as Lorentz or Galilei
invariance and allows for improved, self-consistent approximations in terms of
derivative expansions in Minkowski space.Comment: 32 pages, 5 figures, published versio
Renormalization of Quantum Fields on the Lightcone Worldsheet I: Scalar Fields
We show that the lightcone worldsheet formalism, constructed to represent the
sum of the bare planar diagrams of scalar \phi^3 field theory, survives the
renormalization procedure in space-time dimensions D not greater than 6.
Specifically this means that all the counter-terms, necessary to produce a
successful renormalized perturbation expansion to all orders, can be
represented as local terms in the lightcone worldsheet action. Because the
worldsheet regulator breaks Lorentz invariance, we find the need for two
non-covariant counter-terms, in addition to the usual mass, coupling and wave
function renormalization. One of these can be simply interpreted as a rescaling
of transverse coordinates with respect to longitudinal coordinates. The second
one introduces couplings between the matter and ghost worldsheet fields on the
boundaries.Comment: 18 pages, 3 figure
Store-and-forward based methods for the signal control problem in large-scale congested urban road networks
The problem of designing network-wide traffic signal control strategies for large-scale congested urban road networks is considered. One known and two novel methodologies, all based on the store-and-forward modeling paradigm, are presented and compared. The known methodology is a linear multivariable feedback regulator derived through the formulation of a linear-quadratic optimal control problem. An alternative, novel methodology consists of an open-loop constrained quadratic optimal control problem, whose numerical solution is achieved via quadratic programming. Yet a different formulation leads to an open-loop constrained nonlinear optimal control problem, whose numerical solution is achieved by use of a feasible-direction algorithm. A preliminary simulation-based investigation of the signal control problem for a large-scale urban road network using these methodologies demonstrates the comparative efficiency and real-time feasibility of the developed signal control methods
Ultraviolet Divergences in Cosmological Correlations
A method is developed for dealing with ultraviolet divergences in
calculations of cosmological correlations, which does not depend on dimensional
regularization. An extended version of the WKB approximation is used to analyze
the divergences in these calculations, and these divergences are controlled by
the introduction of Pauli--Villars regulator fields. This approach is
illustrated in the theory of a scalar field with arbitrary self-interactions in
a fixed flat-space Robertson--Walker metric with arbitrary scale factor .
Explicit formulas are given for the counterterms needed to cancel all
dependence on the regulator properties, and an explicit prescription is given
for calculating finite regulator-independent correlation functions. The
possibility of infrared divergences in this theory is briefly considered.Comment: References added on various regularization methods. Improved
discussion of further issues. 26 pages, 1 figur
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