280 research outputs found
Worldline approach to vector and antisymmetric tensor fields
The N=2 spinning particle action describes the propagation of antisymmetric
tensor fields, including vector fields as a special case. In this paper we
study the path integral quantization on a one-dimensional torus of the N=2
spinning particle coupled to spacetime gravity. The action has a local N=2
worldline supersymmetry with a gauged U(1) symmetry that includes a
Chern-Simons coupling. Its quantization on the torus produces the one-loop
effective action for a single antisymmetric tensor. We use this worldline
representation to calculate the first few Seeley-DeWitt coefficients for
antisymmetric tensor fields of arbitrary rank in arbitrary dimensions. As side
results we obtain the correct trace anomaly of a spin 1 particle in four
dimensions as well as exact duality relations between differential form gauge
fields. This approach yields a drastic simplification over standard heat-kernel
methods. It contains on top of the usual proper time a new modular parameter
implementing the reduction to a single tensor field. Worldline methods are
generically simpler and more efficient in perturbative computations then
standard QFT Feynman rules. This is particularly evident when the coupling to
gravity is considered.Comment: 30 pages, 5 figures, references adde
Higher spin fields from a worldline perspective
Higher spin fields in four dimensions, and more generally conformal fields in
arbitrary dimensions, can be described by spinning particle models with a
gauged SO(N) extended supergravity on the worldline. We consider here the
one-loop quantization of these models by studying the corresponding partition
function on the one-dimensional torus. After gauge fixing the supergravity
multiplet, the partition function reduces to an integral over the corresponding
moduli space which is computed using orthogonal polynomial techniques. We
obtain a compact formula which gives the number of physical degrees of freedom
for all N in all dimensions. As an aside we compute the physical degrees of
freedom of the SO(4) = SU(2)xSU(2) model with only a SU(2) factor gauged, which
has attracted some interest in the literature.Comment: 21 page
Scalar Field with Robin Boundary Conditions in the Worldline Formalism
The worldline formalism has been widely used to compute physical quantities
in quantum field theory. However, applications of this formalism to quantum
fields in the presence of boundaries have been studied only recently. In this
article we show how to compute in the worldline approach the heat kernel
expansion for a scalar field with boundary conditions of Robin type. In order
to describe how this mechanism works, we compute the contributions due to the
boundary conditions to the coefficients A_1, A_{3/2} and A_2 of the heat kernel
expansion of a scalar field on the positive real line.Comment: Presented at 8th Workshop on Quantum Field Theory Under the Influence
of External Conditions (QFEXT 07), Leipzig, Germany, 16-21 Sep 200
Effective action for Einstein-Maxwell theory at order RF**4
We use a recently derived integral representation of the one-loop effective
action in Einstein-Maxwell theory for an explicit calculation of the part of
the effective action containing the information on the low energy limit of the
five-point amplitudes involving one graviton, four photons and either a scalar
or spinor loop. All available identities are used to get the result into a
relatively compact form.Comment: 13 pages, no figure
Consistency conditions and trace anomalies in six dimensions
Conformally invariant quantum field theories develop trace anomalies when
defined on curved backgrounds. We study again the problem of identifying all
possible trace anomalies in d=6 by studying the consistency conditions to
derive their 10 independent solutions. It is known that only 4 of these
solutions represent true anomalies, classified as one type A anomaly, given by
the topological Euler density, and three type B anomalies, made up by three
independent Weyl invariants. However, we also present the explicit expressions
of the remaining 6 trivial anomalies, namely those that can be obtained by the
Weyl variation of local functionals. The knowledge of the latter is in general
necessary to disentangle the universal coefficients of the type A and B
anomalies from calculations performed on concrete models.Comment: 16 pages, LaTe
Photon-graviton mixing in an electromagnetic field
Einstein-Maxwell theory implies the mixing of photons with gravitons in an
external electromagnetic field. This process and its possible observable
consequences have been studied at tree level for many years. We use the
worldline formalism for obtaining an exact integral representation for the
one-loop corrections to this amplitude due to scalars and fermions. We study
the structure of this amplitude, and obtain exact expressions for various
limiting cases.Comment: 13 pages, 1 figure, talk given by C. Schubert at QFEXT07, Leipzig,
17-21 Sep 2007, final published version (slightly extended
The Hydrodynamics of M-Theory
We consider the low energy limit of a stack of N M-branes at finite
temperature. In this limit, the M-branes are well described, via the AdS/CFT
correspondence, in terms of classical solutions to the eleven dimensional
supergravity equations of motion. We calculate Minkowski space two-point
functions on these M-branes in the long-distance, low-frequency limit, i.e. the
hydrodynamic limit, using the prescription of Son and Starinets
[hep-th/0205051]. From these Green's functions for the R-currents and for
components of the stress-energy tensor, we extract two kinds of diffusion
constant and a viscosity. The N dependence of these physical quantities may
help lead to a better understanding of M-branes.Comment: 1+19 pages, references added, section 5 clarified, eq. (72) correcte
Worldline approach to quantum field theories on flat manifolds with boundaries
We study a worldline approach to quantum field theories on flat manifolds
with boundaries. We consider the concrete case of a scalar field propagating on
R_+ x R^{D-1} which leads us to study the associated heat kernel through a one
dimensional (worldline) path integral. To calculate the latter we map it onto
an auxiliary path integral on the full R^D using an image charge. The main
technical difficulty lies in the fact that a smooth potential on R_+ x R^{D-1}
extends to a potential which generically fails to be smooth on R^D. This
implies that standard perturbative methods fail and must be improved. We
propose a method to deal with this situation. As a result we recover the known
heat kernel coefficients on a flat manifold with geodesic boundary, and compute
two additional ones, A_3 and A_{7/2}. The calculation becomes sensibly harder
as the perturbative order increases, and we are able to identify the complete
A_{7/2} with the help of a suitable toy model. Our findings show that the
worldline approach is viable on manifolds with boundaries. Certainly, it would
be desirable to improve our method of implementing the worldline approach to
further simplify the perturbative calculations that arise in the presence of
non-smooth potentials.Comment: 19 pages, 6 figures. Minor rephrasing of a few sentences, references
added. Version accepted by JHE
Half-integer Higher Spin Fields in (A)dS from Spinning Particle Models
We make use of O(2r+1) spinning particle models to construct linearized
higher-spin curvatures in (A)dS spaces for fields of arbitrary half-integer
spin propagating in a space of arbitrary (even) dimension: the field
potentials, whose curvatures are computed with the present models, are
spinor-tensors of mixed symmetry corresponding to Young tableaux with D/2 - 1
rows and r columns, thus reducing to totally symmetric spinor-tensors in four
dimensions. The paper generalizes similar results obtained in the context of
integer spins in (A)dS.Comment: 1+18 pages; minor changes in the notation, references updated.
Published versio
Photon-Graviton Amplitudes from the Effective Action
We report on the status of an ongoing effort to calculate the complete
one-loop low-energy effective actions in Einstein-Maxwell theory with a massive
scalar or spinor loop, and to use them for obtaining the explicit form of the
corresponding M-graviton/N-photon amplitudes. We present explicit results for
the effective actions at the one-graviton four-photon level, and for the
amplitudes at the one-graviton two-photon level. As expected on general
grounds, these amplitudes relate in a simple way to the corresponding
four-photon amplitudes. We also derive the gravitational Ward identity for the
1PI one-graviton -- N photon amplitude.Comment: 9 pages, 2 figures, talk given by C. Schubert at "Supersymmetries and
Quantum Symmetries - SQS`2011", JINR Dubna, July 18 - 23, 2011 (to appear in
the Proceedings
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