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

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

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

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

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

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