Olindo Corradini

Spinning particles and higher spin fields on (A)dS backgrounds

Spinning particle models can be used to describe higher spin fields in first quantization. In this paper we discuss how spinning particles with gauged O(N) supersymmetries on the worldline can be consistently coupled to conformally flat spacetimes, both at the classical and at the quantum level. In particular, we consider canonical quantization on flat and on (A)dS backgrounds, and discuss in detail how the constraints due to the worldline gauge symmetries produce geometrical equations for higher spin fields, i.e. equations written in terms of generalized curvatures. On flat space the algebra of constraints is linear, and one can integrate part of the constraints by introducing gauge potentials. This way the equivalence of the geometrical formulation with the standard formulation in terms of gauge potentials is made manifest. On (A)dS backgrounds the algebra of constraints becomes quadratic, nevertheless one can use it to extend much of the previous analysis to this case. In particular, we derive general formulas for expressing the curvatures in terms of gauge potentials and discuss explicitly the cases of spin 2, 3 and 4.

dimensional regularization for N=1 supersymmetric sigma models and the worldline formalism

We generalize the worldline formalism to include spin 1/2 fields coupled to gravity. To this purpose we first extend dimensional regularization to supersymmetric nonlinear sigma models in one dimension. We consider a finite propagation time and find that dimensional regularization is a manifestly supersymmetric regularization scheme, since the classically supersymmetric action does not need any counterterm to preserve worldline supersymmetry. We apply this regularization scheme to the worldline description of Dirac fermions coupled to gravity. We first compute the trace anomaly of a Dirac fermion in 4 dimensions, providing an additional check on the regularization with finite propagation time. Then we come to the main topic and consider the one-loop effective action for a Dirac field in a gravitational background. We describe how to represent this effective action as a worldline path integral and compute explicitly the one- and two-point correlation functions, i.e. the spin 1/2 particle contribution to the graviton tadpole and graviton self-energy. These results are presented for the general case of a massive fermion. It is interesting to note that in the worldline formalism the coupling to gravity can be described entirely in terms of the metric, avoiding the introduction of a vielbein. Consequently, the fermion--graviton vertices are always linear in the graviton, just like the standard coupling of fermions to gauge fields.

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 circle. 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) × SU(2) model with only a SU(2) factor gauged, which has attracted some interest in the literature.

Induced gravity on intersecting brane worlds: Maximally symmetric solutions

We explore models of intersecting brane worlds with induced gravity terms on codimension-one branes and on their intersection. Maximally symmetric solutions for the branes and the intersection are found. We find new self-accelerating solutions. In a 6D spacetime, the solutions realize the seesaw modification of gravity where the UV scale of the modification to 4D gravity is determined by 6D Planck scale given by

Gravity on a 3-brane in 6D bulk

{M}_{6}\ensuremath{\sim}{10}^{\ensuremath{-}3}\text{ }\text{ }\mathrm{eV}

Induced gravity on intersecting brane worlds. II, Cosmology

and the IR scale of the modification is determined by

BRST treatment of zero modes for the worldline formalism in curved space

{M}_{6}^{2}/{M}_{4}\ensuremath{\sim}{H}_{0}\ensuremath{\sim}{10}^{\ensuremath{-}42}\text{ }\text{ }\mathrm{GeV}

Detours and Paths: BRST Complexes and Worldline Formalism

, where

Localized gravity and higher curvature terms

{H}_{0}

Mode regularization of the configuration space path integral in curved space

is the present-day Hubble scale. We find that it is increasingly difficult to construct phenomenologically viable models in higher-dimensional spacetime due to the necessity to have the lower value for the fundamental Planck scale to realize the late time acceleration. It is found that the system also admits self-tuning solutions where the tension at the intersection does not change the geometry of the intersection. The induced gravity terms can avoid the necessity to compactify the extra dimensions. Finally, we discuss the possibility to have ordinary matter at the intersection, without introducing any regularization, using the induced gravity terms.