321 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
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
Quantum theory of massless (p,0)-forms
We describe the quantum theory of massless (p,0)-forms that satisfy a
suitable holomorphic generalization of the free Maxwell equations on Kaehler
spaces. These equations arise by first-quantizing a spinning particle with a
U(1)-extended local supersymmetry on the worldline. Dirac quantization of the
spinning particle produces a physical Hilbert space made up of (p,0)-forms that
satisfy holomorphic Maxwell equations coupled to the background Kaehler
geometry, containing in particular a charge that measures the amount of
coupling to the U(1) part of the U(d) holonomy group of the d-dimensional
Kaehler space. The relevant differential operators appearing in these equations
are a twisted exterior holomorphic derivative and its hermitian conjugate
(twisted Dolbeault operators with charge q). The particle model is used to
obtain a worldline representation of the one-loop effective action of the
(p,0)-forms. This representation allows to compute the first few heat kernel
coefficients contained in the local expansion of the effective action and to
derive duality relations between (p,0) and (d-p-2,0)-forms that include a
topological mismatch appearing at one-loop.Comment: 32 pages, 3 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
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
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
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
Bergman Kernel from Path Integral
We rederive the expansion of the Bergman kernel on Kahler manifolds developed
by Tian, Yau, Zelditch, Lu and Catlin, using path integral and perturbation
theory, and generalize it to supersymmetric quantum mechanics. One physics
interpretation of this result is as an expansion of the projector of wave
functions on the lowest Landau level, in the special case that the magnetic
field is proportional to the Kahler form. This is relevant for the quantum Hall
effect in curved space, and for its higher dimensional generalizations. Other
applications include the theory of coherent states, the study of balanced
metrics, noncommutative field theory, and a conjecture on metrics in black hole
backgrounds. We give a short overview of these various topics. From a
conceptual point of view, this expansion is noteworthy as it is a geometric
expansion, somewhat similar to the DeWitt-Seeley-Gilkey et al short time
expansion for the heat kernel, but in this case describing the long time limit,
without depending on supersymmetry.Comment: 27 page
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
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