396 research outputs found
U(N|M) quantum mechanics on Kaehler manifolds
We study the extended supersymmetric quantum mechanics, with supercharges
transforming in the fundamental representation of U(N|M), as realized in
certain one-dimensional nonlinear sigma models with Kaehler manifolds as target
space. We discuss the symmetry algebra characterizing these models and, using
operatorial methods, compute the heat kernel in the limit of short propagation
time. These models are relevant for studying the quantum properties of a
certain class of higher spin field equations in first quantization.Comment: 21 pages, a reference adde
Conformal anomaly of (2,0) tensor multiplet in six dimensions and AdS/CFT correspondence
We compute the conformal anomaly of free d=6 superconformal (2,0) tensor
multiplet on generic curved background. Up to a trivial covariant
total-derivative term, it is given by the sum of the type A part proportional
to the 6-d Euler density, and the type B part containing three independent Weyl
invariants. Multiplied by factor 4N^3, the type B part of the anomaly
reproduces exactly the corresponding part of the conformal anomaly of large N
multiple M5-brane (2,0) theory as predicted (hep-th/9806087) by the AdS/CFT
correspondence. The coefficients of the type A anomaly differ by the factor 4/7
x 4 N^3, so that the free tensor multiplet anomaly does not vanish on a
Ricci-flat background. The coefficient 4N^3 is the same as found
(hep-th/9703040) in the comparison of the tensor multiplet theory and the d=11
supergravity results for the absorption cross-sections of gravitons by M5
branes, and in the comparison (hep-th/9911135) of 2- and 3-point stress tensor
correlators of the free tensor multiplet with the AdS_7 supergravity
predictions. The reason for this coincidence is that the three Weyl-invariant
terms in the anomaly are related to the and terms in the near flat
space expansion of the corresponding non-local effective action, and thus to
the 2-point and 3-point stress tensor correlators in flat background. At the
same time, the type A anomaly is related to the term in the non-local
part of the effective action, i.e. to a certain structure in the 4-point
correlation function of stress tensors.Comment: 20 pages, latex. v2: minor corrections, references adde
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
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
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
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
Integral representations combining ladders and crossed-ladders
We use the worldline formalism to derive integral representations for three
classes of amplitudes in scalar field theory: (i) the scalar propagator
exchanging N momenta with a scalar background field (ii) the "half-ladder" with
N rungs in x - space (iii) the four-point ladder with N rungs in x - space as
well as in (off-shell) momentum space. In each case we give a compact
expression combining the N! Feynman diagrams contributing to the amplitude. As
our main application, we reconsider the well-known case of two massive scalars
interacting through the exchange of a massless scalar. Applying asymptotic
estimates and a saddle-point approximation to the N-rung ladder plus crossed
ladder diagrams, we derive a semi-analytic approximation formula for the lowest
bound state mass in this model.Comment: 39 pages, 10 pdf 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
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
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