SPIN-$\frac{3}{2}$ POTENTIALS IN BACKGROUNDS WITH BOUNDARY

Abstract

Potentials in Backgrounds with Boundary

One-loop divergences in simple supergravity: Boundary effects

“…(i) Choice of background four-geometry. This may be flat Euclidean four-space, which is relevant for massless theories [12], or the de Sitter four-sphere [13], which is relevant for inflationary cosmology [14], or more general curved backgrounds. The latter appear interesting for a better understanding of quantum field theory in curved space-time.…”

Effect of Activation of Oxygen by Electron Cyclotron Resonance Plasma on the Incorporation of Pb in the Deposition of Pb(Zr,Ti)O 3 Films by DC Magnetron Reactive Sputtering

“…In particular, the background 4-manifold M can be taken to be flat Euclidean 4-space bounded by a 3-sphere. The analysis of flat backgrounds is indeed relevant both for Euclidean field theory [11] and for the analysis of massless supergravity models in the presence of boundaries [12]. In the de Donder gauge, the boundary conditions on the metric perturbations which are invariant under gauge transformations then take the form [8,9] [h ij ] ∂M = 0 (1.1) ∂h 00 ∂τ…”

Local boundary conditions in quantum supergravity

“…The problem of a consistent formulation of quantum supergravity on manifolds with boundary is still receiving careful consideration in the current literature [1][2][3][4]. In particular, many efforts have been produced to understand whether simple supergravity is one-loop finite (or even finite to all orders of perturbation theory [3]) in the presence of boundaries.…”

“…In the analysis of such an issue, the first problem consists, of course, in a careful choice of boundary conditions. For massless gravitino potentials, which are the object of our investigation, these may be non-local of the spectral type [5] or local [1][2][3][4].…”

“…Using two-component spinor notation, and referring the reader to Refs. [3,11] for notation and background material, we here represent the spin-3 2 potential by a pair of independent spinor-valued one-forms ψ A µ , ψ A ′ µ in a Riemannian 4manifold which is taken to be flat Euclidean 4-space bounded by two concentric 3-spheres [2,4]. Denoting by S I and S F the boundary 3-spheres, with radii a and b respectively (here b > a), the local boundary conditions proposed in Ref.…”