387 research outputs found
Quantum theories of (p,q)-forms
We describe quantum theories for massless (p,q)-forms living on Kaehler
spaces. In particular we consider four different types of quantum theories: two
types involve gauge symmetries and two types are simpler theories without gauge
invariances. The latter can be seen as building blocks of the former. Their
equations of motion can be obtained in a natural way by first-quantizing a
spinning particle with a U(2)-extended supersymmetry on the worldline. The
particle system contains four supersymmetric charges, represented quantum
mechanically by the Dolbeault operators and their hermitian conjugates. After
studying how the (p,q)-form field theories emerge from the particle system, we
investigate their one loop effective actions, identify corresponding heat
kernel coefficients, and derive exact duality relations. The dualities are seen
to include mismatches related to topological indices and analytic torsions,
which are computed as Tr(-1)^F and Tr[(-1)^F F] in the first quantized
supersymmetric nonlinear sigma model for a suitable fermion number operator F.Comment: 44 pages, 2 figures, a reference adde
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
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
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
A Hierarchy of Superstrings
We construct a hierarchy of supersymmetric string theories by showing that
the general N-extended superstrings may be viewed as a special class of the
(N+1)-extended superstrings. As a side result, we find a twisted (N+2)
superconformal algebra realized in the N-extended string.Comment: 9 pages, LaTex, NBI-HE-94-2
Detours and Paths: BRST Complexes and Worldline Formalism
We construct detour complexes from the BRST quantization of worldline
diffeomorphism invariant systems. This yields a method to efficiently extract
physical quantum field theories from particle models with first class
constraint algebras. As an example, we show how to obtain the Maxwell detour
complex by gauging N=2 supersymmetric quantum mechanics in curved space. Then
we concentrate on first class algebras belonging to a class of recently
introduced orthosymplectic quantum mechanical models and give generating
functions for detour complexes describing higher spins of arbitrary symmetry
types. The first quantized approach facilitates quantum calculations and we
employ it to compute the number of physical degrees of freedom associated to
the second quantized, field theoretical actions.Comment: 1+35 pages, 1 figure; typos corrected and references added, published
versio
On the low energy limit of one loop photon-graviton amplitudes
We present first results of a systematic study of the structure of the low
energy limit of the one-loop photon-graviton amplitudes induced by massive
scalars and spinors. Our main objective is the search of KLT-type relations
where effectively two photons merge into a graviton. We find such a relation at
the graviton-photon-photon level. We also derive the diffeomorphism Ward
identity for the 1PI one graviton - N photon amplitudes.Comment: 14 pages, 1 figure. Final version to be published in Physics Letters
Violation of the phase space general covariance as a diffeomorphism anomaly in quantum mechanics
We consider a topological quantum mechanics described by a phase space path
integral and study the 1-dimensional analog for the path integral
representation of the Kontsevich formula. We see that the naive bosonic
integral possesses divergences, that it is even naively non-invariant and thus
is ill-defined. We then consider a super-extension of the theory which
eliminates the divergences and makes the theory naively invariant. This
super-extension is equivalent to the correct choice of measure and was
discussed in the literature. We then investigate the behavior of this extended
theory under diffeomorphisms of the extended phase space and despite of its
naive invariance find out that the theory possesses anomaly under nonlinear
diffeomorphisms. We localize the origin of the anomaly and calculate the lowest
nontrivial anomalous contribution.Comment: 36 page
The BRST Operator for the Large Superconformal Algebra
We review the detailed structure of the large superconformal algebra,
and construct its BRST operator which constitutes the main object for analyzing
strings. We then derive the general condition for the nilpotency of the
BRST operator and show that there exists a line of critical string
theories.Comment: Latex file, 16 pages, NBI-HE-94-1
Simplified Method for Trace Anomaly Calculations in d=6 and d<6
We discuss a simplified method for computing trace anomalies in d=6 and d<6
dimensions. It is known that in the quantum mechanical approach trace anomalies
in d dimensions are given by a (1+d/2)-loop computation in an auxiliary 1d
sigma model with arbitrary geometry. We show how one can obtain the same
information using a simpler d/2-loop calculation on an arbitrary geometry
supplemented by a (1+d/2)-loop calculation on the simplified geometry of a
maximally symmetric space.Comment: 8 pages, LaTeX, corrected minor misprints, references adde
- âŠ