We propose an alternative for the Clebsch decomposition of currents in fluid mechanics, in terms of complex potentials taking values in a Kähler manifold. We reformulate classical relativistic fluid mechanics in terms of these complex potentials and rederive the existence of an infinite set of conserved currents. We perform a canonical analysis to find the explicit form of the algebra of conserved charges. The Kähler-space formulation of the theory has a natural supersymmetric extension in 4-D space-time. It contains a conserved current, but also a number of additional fields complicating the interpretation. Nevertheless, we show that an infinite set of conserved currents emerges in the vacuum sector of the additional fields. This sector can therefore be identified with a regime of supersymmetric fluid mechanics. Explicit expressions for the current and the density are obtained. *

This paper discusses a procedure for the consistent coupling of gaugeand matter superfields to supersymmetric sigma-models on symmetric coset spaces of Kähler type. We exhibit the finite isometry transformations and the corresponding Kähler transformations. These lead to the construction of a generalized type of Killing potentials. In certain cases a charge quantization condition needs to be imposed to guarantee the global existence of a line bundle on a coset space. The results are applied to the explicit construction of sigma-models on cosets SO(2N )/U (N ). Only a finite number of these models can consistently incorporate matter in representations descending from the spinorial representations of SO(2N ). We investigate in detail some aspects of the vacuum structure of the gauged SO(10)/U (5) theory, with surprising results: the fully gauged minimal anomaly-free model is shown be singular, as the kinetic terms of the quasi-Goldstone fermions vanish in the vacuum. Gauging only the linear isometry group SU (5) × U (1), or one of its subgroups, can give a physically well-behaved theory. With gauged U (1) this requires the Fayet-Iliopoulos term to take values in a specific limited range.

We present a covariant and supersymmetric theory of relativistic hydrodynamics in four-dimensional Minkowski space.Comment: 5 pages, revte

We perform a supergraph computation of the effective Kähler potential at one and two loops for general four dimensional N = 1 supersymmetric theories described by arbitrary Kähler potential, superpotential and gauge kinetic function. We only insist on gauge invariance of the Kähler potential and the superpotential as we heavily rely on its consequences in the quantum theory. However, we do not require gauge invariance for the gauge kinetic functions, so that our results can also be applied to anomalous theories that involve the Green-Schwarz mechanism. We illustrate our two loop results by considering a few simple models: the (non-)renormalizable Wess-Zumino model and Super Quantum Electrodynamics.

We study the renormalization of (softly) broken supersymmetric theories at the one loop level in detail. We perform this analysis in a superspace approach in which the supersymmetry breaking interactions are parameterized using spurion insertions. We comment on the uniqueness of this parameterization. We compute the one loop renormalization of such theories by calculating superspace vacuum graphs with multiple spurion insertions. To preform this computation efficiently we develop algebraic properties of spurion operators, that naturally arise because the spurions are often surrounded by superspace projection operators. Our results are general apart from the restrictions that higher super covariant derivative terms and some finite effects due to non-commutativity of superfield dependent mass matrices are ignored. One of the soft potentials induces renormalization of the Kähler potential.