Toward an Off - Shell 11D Supergravity Limit of M - Theory

We demonstrate that in addition to the usual fourth-rank superfield $(W_{a b c d})$ which describes the on-shell theory, a spinor superfield (J_\a ) can be introduced into the 11D geometrical tensors with engineering dimensions less or equal to one in such a way to satisfy the Bianchi identities in superspace. The components arising from J_\a are identified as some of the auxiliary fields required for a full off-shell formulation. Our result indicates that eleven dimensional supergravity does not have to be completely on-shell. The \k\-symmetry of the supermembrane action in the presence of our partial off-shell supergravity background is also confirmed. Our modifications to eleven-dimensional supergravity theory are thus likely relevant for M-theory. We suggest our proposal as a significant systematic off-shell generalization of eleven-dimensional supergravity theory.Comment: 13 pages, LATEX (all macros included. No figures

Polarized QED splittings of massive fermions and dipole subtraction for non-collinear-safe observables

Building on earlier work, the dipole subtraction formalism for photonic corrections is extended to various photon--fermion splittings where the resulting collinear singularities lead to corrections that are enhanced by logarithms of small fermion masses. The difference to the earlier treatment of photon radiation is that now no cancellation of final-state singularities is assumed, i.e. we allow for non-collinear-safe final-state radiation. Moreover, we consider collinear fermion production from incoming photons, forward-scattering of incoming fermions, and collinearly produced fermion-antifermion pairs. For all cases we also provide the corresponding formulas for the phase-space slicing approach, and particle polarization is supported for all relevant situations. A comparison of numerical results obtained with the proposed subtraction procedure and the slicing method is explicitly performed for the sample process e- gamma -> e- mu- mu+.Comment: 44 pages, late