F. Paul Esposito

Higher-derivative terms in N = 2 supersymmetric effective actions

We show how to systematically construct higher-derivative terms in effective actions in harmonic superspace despite the infinite redundancy in their description due to the infinite number of auxiliary fields. Making an assumption about the absence of certain superspace Chern-Simons-like terms involving vector multiplets, we write all 3- and 4-derivative terms on Higgs, Coulomb, and mixed branches. Among these terms are several with only holomorphic dependence on fields, and at least one satisfies a non-renormalization theorem. These holomorphic terms include a novel 3-derivative term on mixed branches given as an integral over 3/4 of superspace. As an illustration of our method, we search for Wess-Zumino terms in the low energy effective action of N=2 supersymmetric QCD. We show that such terms occur only on mixed branches. We also present an argument showing that the combination of space-time locality with supersymmetry implies locality in the anticommuting superspace coordinates of for unconstrained superfields.

Exact solution for the gravitational field of a charged, magnetized, spinning mass

A family of solutions of the Einstein-Maxwell field equations is presented, corresponding to the exterior of stationaryaxisymmetric sources with charge, mass, angular momentum, and magnetic dipole moment. The Riemann tensor vanishes asymptotically for each member of the family; some solutions are asymptotically flat and some have NUT-like behavior asymptotically. For the asymptotically flat solutions, the gyromagnetic ratio may vary from zero to one. The corresponding value for the Kerr-Newman solution is one. A method for generating infinite chains of families of solutions of the Einstein-Maxwell equations is described.

TYPE IIB ORIENTIFOLDS WITH DISCRETE TORSION

We consider compact four-dimensional ZN × ZM type IIB orientifolds, for certain values of N and M. We allow the additional feature of discrete torsion and discuss the modification of the consistency conditions arising from tadpole cancellation. We point out the differences between the cases with and without discrete torsion.

On superspace Chern-Simons-like terms

We search for superspace Chern-Simons-like higher-derivative terms in the low energy effective actions of supersymmetric theories in four dimensions. Superspace Chern-Simons-like terms are those gauge-invariant terms which cannot be written solely in terms of field strength superfields and covariant derivatives, but in which a gauge potential superfield appears explicitly. We find one class of such four-derivative terms with N = 2 supersymmetry which, though locally on the Coulomb branch can be written solely in terms of field strengths, globally cannot be. These terms are classified by certain Dolbeault cohomology classes on the moduli space. We include a discussion of other examples of terms in the effective action involving global obstructions on the Coulomb branch.

General relativistic magnetofluids

General relativistic hydromagnetic systems are studied in the infinite conductivity limit. It is shown that when the frozen‐in magnetic field lies in surfaces of constant pressure, the fluid acceleration and magnetic field are orthogonal. The theorem is proved that a shear‐free infinite conductivity magnetofluid is irrotational if and only if the Weyl tensor is pure electric type. A restricted steady state is formulated and discussed, and within that state it is shown that an infinite conductivity magnetofluid cannot be electrically neutral.

HIGHER DERIVATIVE TERMS IN N=2 SUSY EFFECTIVE ACTIONS

Harmonic superspace can be used to construct higher derivative terms in N=2 supersymmetric effective actions despite the infinite redundancy in their description due to the infinite number of auxiliary fields. We are able to write down all of the 3- and 4-derivative terms on the Higgs, Coulomb, and mixed branches, modulo the possible existence of superspace Chern-Simons-like terms, which we discuss. Many of the terms we find are holomorphic, and at least one is shown to not receive quantum corrections.

A scalar invariant and the local geometry of a class of static spacetimes

The scalar invariant, I≡Rμνρσ;δ Rμνρσ;δ, constructed from the covariant derivative of the curvature tensor is used to probe the local geometry of static spacetimes which are also Einstein spaces. We obtain an explicit form of this invariant, exploiting the local warp-product structure of a 4-dimensional static spacetime, (3)Σ × f, where (3)Σ is the riemannian hypersurface orthogonal to a timelike Killing vector field with norm given by a positive function, f: (3)Σ. For a static spacetime which is an Einstein space, it is shown that the locally measurable scalar, I, contains a term which vanishes if and only if (3)Σ is conformally flat; also, the vanishing of this term implies (a) (3)Σ is locally foliated by level surfaces of f, (2)S, which are totally umbilic spaces of constant curvature, and (b) (3)Σ is locally a warp-product space, × r(f) (2)S, for some function r(f). Futhermore, if (3)Σ is conformally flat it follows that every non-trivial static solution of the vacuum Einstein equation with a cosmological constant, is either Nariai-type or Kottler-type — the classes of spacetimes relevant to quantum aspects of gravity.

The Weyl tensor and stationary electrovac space–times

It is shown that static electrovac spaces admit only static electric type Maxwell fields, and it is proved that a necessary and sufficient condition for a stationary electrovac space–time to be static is that the Weyl tensor and the Maxwell field tensor both be pure electric type.

Conserved quantities for stationary Einstein-Maxwell space-times☆

Abstract We show that every stationary Einstein-Maxwell space-time has eight divergence-free vector fields and we isolate these in general form. The vector fields and associated conserved quantities are calculated for several families of space-times.