Augmented Superfield Approach to Gauge-invariant Massive 2-Form Theory

We discuss the complete sets of the off-shell nilpotent (i.e. s^2_{(a)b} = 0) and absolutely anticommuting (i.e. s_b s_{ab} + s_{ab} s_b = 0) Becchi-Rouet-Stora-Tyutin (BRST) (s_b) and anti-BRST (s_{ab}) symmetries for the (3+1)-dimensional (4D) gauge-invariant massive 2-form theory within the framework of augmented superfield approach to BRST formalism. In this formalism, we obtain the coupled (but equivalent) Lagrangian densities which respect both BRST and anti-BRST symmetries on the constrained hypersurface defined by the Curci-Ferrari type conditions. The absolute anticommutativity property of the (anti-)BRST transformations (and corresponding generators) is ensured by the existence of the Curci-Ferrari type conditions which emerge very naturally in this formalism. Furthermore, the gauge-invariant restriction plays a decisive role in deriving the proper (anti-)BRST transformations for the St{\"u}ckelberg-like vector field.Comment: LaTeX file, 22 pages, no figures, version to appear in Eur. Phys. J. C (2017

Gravitino Zero Modes on U(1)_R Strings

We consider theories with a spontaneously broken gauged R-symmetry, which can only occur in supergravity models. These give rise to cosmic R-strings upon which gravitino zero modes can exist. We construct solutions to the Rarita-Schwinger spin-3/2 equation describing the gravitino in the field of these cosmic strings and show that under some conditions these solutions may give rise to gravitino currents on the string. We discuss further mathematical and physical questions associated with these solutions.Comment: 18 pages, uses revte

Mixed and discontinuous finite volume element schemes for the optimal control of immiscible flow in porous media

We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous finite volume element methods in combination with the optimise-then-discretise approach for the approximation of the optimal control problem, leading to nonsymmetric algebraic systems, and employing minimum regularity requirements. Estimates for the error (between a local reference solution of the infinite dimensional optimal control problem and its hybrid approximation) measured in suitable norms are derived, showing optimal orders of convergence