1,720,998 research outputs found
Spinning particle approach to higher spin field theory
No full textWe shortly review on the connection between higher-spin gauge field theories and supersymmetric spinning particle models. In such approach the higher spin equations of motion are linked to the first-class constraint algebra associated with the quantization of particle models. Here we consider a class of spinning particle models characterized by local O(N)-extended supersymmetry since these models are known to provide an alternative approach to the geometric formulation of higher spin field theory. We describe the canonical quantization of the models in curved target space and discuss the obstructions that appear in presence of an arbitrarily curved background. We then point out the special role that conformally flat spaces appear to have in such models and present a derivation of the higher-spin curvatures for maximally symmetric spaces
A Monte Carlo approach to the worldline formalism in curved space
Full text linkWe present a numerical method to evaluate worldline (WL) path integrals defined on a curved Euclidean space, sampled with Monte Carlo (MC) techniques. In particular, we adopt an algorithm known as YLOOPS with a slight modification due to the introduction of a quadratic term which has the function of stabilizing and speeding up the convergence. Our method, as the perturbative counterparts, treats the non-trivial measure and deviation of the kinetic term from flat, as interaction terms. Moreover, the numerical discretization adopted in the present WLMC is realized with respect to the proper time of the associated bosonic point-particle, hence such procedure may be seen as an analogue of the time-slicing (TS) discretization already introduced to construct quantum path integrals in curved space. As a result, a TS counter-term is taken into account during the computation. The method is tested against existing analytic calculations of the heat kernel for a free bosonic point-particle in a D-dimensional maximally symmetric space
One-loop quantum gravity from the N=4 spinning particle
Full text linkWe construct a spinning particle that reproduces the propagation of the graviton on those curved backgrounds which solve the Einstein equations, with or without cosmological constant, i.e. Einstein manifolds. It is obtained by modifying the N=4 supersymmetric spinning particle by relaxing the gauging of the full SO(4) R-symmetry group to a parabolic subgroup, and selecting suitable Chern-Simons couplings on the worldline. We test it by computing the correct one-loop divergencies of quantum gravity in D=4
Quantum Darboux theorem
Full text linkThe problem of computing quantum mechanical propagators can be recast as a computation of a Wilson line operator for parallel transport by a flat connection acting on a vector bundle of wave functions. In this picture, the base manifold is an odd-dimensional symplectic geometry, or quite generically a contact manifold that can be viewed as a "phase-spacetime,"while the fibers are Hilbert spaces. This approach enjoys a "quantum Darboux theorem"that parallels the Darboux theorem on contact manifolds which turns local classical dynamics into straight lines. We detail how the quantum Darboux theorem works for anharmonic quantum potentials. In particular, we develop a novel diagrammatic approach for computing the asymptotics of a gauge transformation that locally makes complicated quantum dynamics trivial
Dressed Dirac propagator from a locally supersymmetric N=1 spinning particle
Full text linkWe study the Dirac propagator dressed by an arbitrary number of photons by means of a worldline approach, which makes use of a supersymmetric spinning particle model on the line, coupled to an external Abelian vector field. We obtain a compact off-shell master formula for the tree level scattering amplitudes associated to the dressed Dirac propagator. In particular, unlike in other approaches, we express the particle fermionic degrees of freedom using a coherent state basis, and consider the gauging of the supersymmetry, which ultimately amounts to integrating over a worldline gravitino modulus, other than the usual worldline einbein modulus which corresponds to the Schwinger time integral. The path integral over the gravitino reproduces the numerator of the dressed Dirac propagator
Dimensional regularization for N= 1 supersymmetric sigma models and the worldline formalism
Full text linkWe 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. © 2003 The American Physical Society
Erratum: Dressed scalar propagator in a non-Abelian background from the worldline formalism (Physical Review D - Particles, Fields, Gravitation and Cosmology (2016) 93 (025035))
No full textLocal unit invariance, back-reacting tractors and the cosmological constant problem
Full text linkWhen physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of fields necessary to keep local unit invariance manifest). The relationship between these weights and masses is through the scalar curvature. As a consequence mass terms are spacetime dependent for off-shell gravitational backgrounds, but happily constant for physical, Einstein manifolds. Unfortunately this introduces a naturalness problem because the scalar curvature is proportional to the cosmological constant. By writing down tractor stress tensors (multiplets built from the standard stress tensor and its first and second derivatives), we show how back-reaction solves this naturalness problem. We also show that classical back-reaction generates an interesting potential for scalar fields. We speculate that a proper description of how physical systems couple to scale, could improve our understanding of naturalness problems caused by the disparity between the particle physics and observed, cosmological constants. We further give some ideas how an ambient description of tractor calculus could lead to a Ricci-flat/CFT correspondence which generalizes the AdS side of Maldacena's duality to a Ricci-flat space of one higher dimension
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