Supersymmetric Spinning Particle Research Articles

A worldline theory for supergravity

The mathcal{N} = 4 supersymmetric spinning particle admits several consistent quantizations, related to the gauging of different subgroups of the SO(4) R-symmetry on the worldline. We construct the background independent BRST quantization for all of these choices which are shown to reproduce either the massless NS-NS spectrum of the string, or Einstein theory with or without the antisymmetric tensor field and/or dilaton corresponding to different restrictions. Quantum consistency of the worldline implies equations of motion for the background which, in addition to the admissible string backgrounds, admit Einstein manifolds with or whithout a cosmological constant. The vertex operators for the Kalb-Ramond, graviton and dilaton fields are obtained from the linear variations of the BRST charge. They produce the physical states by action on the diffeomorphism ghost states.

One-loop quantum gravity from the N particle 4 spinning

We 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 mathcal{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.

Einstein gravity from the mathcal{N}=4 spinning particle

We obtain a manifestly background independent BRST quantization of the mathcal{N}=4 supersymmetric spinning particle. We show that nilpotency of the BRST charge Q implies the Einstein equations admitting a cosmological constant of indefinite sign. The physical graviton states are given by the vertex operator, obtained by an infinitesimal variation of Q, acting on diffeomorphism ghost states. In addition, the tree-point graviton scattering vertex is correctly reproduced by the worldline computation with these vertex operators.

Spinning particle approach to higher spin field theory

We 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.

Quaternionic Kähler Detour Complexes and $${\mathcal{N} = 2}$$ Supersymmetric Black Holes

We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional N= 2 supergravities. By virtue of the c-map, these spinning particles move in quaternionic Kaehler manifolds. Their spinning degrees of freedom describe mini-superspace-reduced supergravity fermions. We quantize these models using BRST detour complex technology. The construction of a nilpotent BRST charge is achieved by using local (worldline) supersymmetry ghosts to generating special holonomy transformations. (An interesting byproduct of the construction is a novel Dirac operator on the superghost extended Hilbert space.) The resulting quantized models are gauge invariant field theories with fields equaling sections of special quaternionic vector bundles. They underly and generalize the quaternionic version of Dolbeault cohomology discovered by Baston. In fact, Baston's complex is related to the BPS sector of the models we write down. Our results rely on a calculus of operators on quaternionic Kaehler manifolds that follows from BRST machinery, and although directly motivated by black hole physics, can be broadly applied to any model relying on quaternionic geometry.

Comment on "BRST quantization of the extended supersymmetric spinning particle"

We show that when properly regularized the divergences appearing in the Feynman kernel of the extended supersymmetric spinning particle do not impose any restriction on the number of supersymmetries and the space-time dimension (for even space-time dimensions).

BRST quantization of the extended supersymmetric spinning particle.

The relativistic spinning-particle model with {ital N}-extended supersymmetry is quantized by the Batalin-Fradkin-Vilkovisky--Becchi-Rouet-Stora-Tyutin procedure. The Feynman kernel is obtained. It is shown that in four-dimensional space-time a massless particle can only have spin 1.

Wave equations for arbitrary spin from quantization of the extended supersymmetric spinning particle

We present the action for a relativistic particle with a gauged N-extended line supersymmetry and show that, upon quantization, it yields a relativistic wave equation for pure spin 1 2 N . A curved-space background is compatible with worldline supersymmetry only for N⩽2.

Superfield formulation of a spinning particle in Riemann-Cartan space-time

A consistent classical Lagrangian for a supersymmetric spinning particle in Riemann-Cartan space-time is presented using superfields in a 2-dimensional superspace. The equations of motion for the position and the spin variables of a particle are investigated in the canonical formalism. The relation with the other models is also discussed.