Paul S. Howe

Superstrings in D=10 from supermembranes in D=11

Abstract The type IIA superstring in ten dimensions is derived from the supermembrane in eleven dimensions by a simultaneous dimensional reduction of the world volume and the spacetime.

The relaxed hypermultiplet: An unconstrained N = 2 superfield theory

Abstract We present an off-shell version of the hypermultiplet, without a central charge or gauge antisymmetric tensors. We give the unconstrained superfield form of the action and its coupling to N = 2 super-Yang-Mills theory. This allows an N = 2 superspace formulation of the N = 4 super-Yang-Mills theory, whose ultraviolet finiteness is then ensured by N = 2 non-renormalization theorems.

Supergravity in superspace

Abstract A comprehensive discussion of the formulation of supergravity theories in superspace is presented. After reviewing the general formalism and the linearized theory, we exhibit a complete solution to the Bianchi identities for all N . This solution still contains a reducible representation of supersymmetry and further constraints are imposed to obtain off-shell conformal supergravity ( N ⩽ 4). N = 1 and 2 off-shell Poincare supergravities are rederived from the corresponding conformal theories. On-shell Poincare supergravity is discussed for all N in superspaces with additional bosonic coordinates.

Twistor spaces for hyper-Kähler manifolds with torsion

Abstract We construct the twistor space associated with an HKT manifold, that is, a hyper-Kahler manifold with torsion, a type of geometry that arises as the target space geometry in two-dimensional sigma models with (4,0) supersymmetry. We show that this twistor space has a natural complex structure and is a holomorphic fibre bundle over the complex projective line with fibre the associated HKT manifold. We also show how the metric and torsion of the HKT manifold can be determined from data on the twistor space by a reconstruction theorem. We give a geometric description of the sigma model (4,0) superfields as holomorphic maps (suitably understood) from a twistorial extension of (4,0) superspace (harmonic superspace) into the twistor space of the sigma model target manifold and write an action for the sigma model in terms of these (4,0) superfields.We construct the twistor space associated with an HKT manifold, that is, a hyper-Kahler manifold with torsion, a type of geometry that arises as the target space geometry in two-dimensional sigma models with (4,0) supersymmetry. We show that this twistor space has a natural complex structure and is a holomorphic fibre bundle over the complex projective line with fibre the associated HKT manifold. We also show how the metric and torsion of the HKT manifold can be determined from data on the twistor space by a reconstruction theorem. We give a geometric description of the sigma model (4,0) superfields as holomorphic maps (suitably understood) from a twistorial extension of (4,0) superspace (harmonic superspace) into the twistor space of the sigma model target manifold and write an action for the sigma model in terms of these (4,0) superfields.

Higher order invariants in extended supergravity

Abstract On-shell linearized extended supergravity is presented in superspace for all N . The formalism is then used in the construction of higher order invariants which may serve as counterterm lagrangians. It is shown that three-loop counterterms exist for N ⩽ 3 and ( N − 1)-loop counterterms for N ⩾ 4. In the full non-linear theory, the presence of a global non-compact symmetry group for N ⩾ 4 does not allow a simple extension of the ( N − 1)-loop term, but N -loop counterterms may be constructed.

A particle mechanics description of antisymmetric tensor fields

In a previous work the authors discussed the action for a massless relativistic point particle with a gauged N-extended worldline supersymmetry that yields, upon quantisation, a relativistic wave equation for pure spin N/2. They present further details, emphasising the N=2 particle model for which a wavefunction with O(2) charge q can be interpreted as the field strength of a (q-1)-form gauge potential. They present extensions of this model that yield field equations for massless and massive antisymmetric tensors in arbitrary spacetime dimension d. They show how to obtain chirality and generalised self-duality conditions.

Auxiliary fields and a superspace lagrangian for linearized ten-dimensional supergravity

Abstract A set of auxiliary fields for linearized ten-dimensional supergravity is presented. The total number of off-shell field components, including those of the physical fields, is 65 664 + 65 664. This set of fields has a simple description in terms of two superfields. A superspace lagrangian which leads to the correct equations of motion is given.

Superconformal ward identities and N=2 Yang-Mills theory

Abstract A reformulation of the superconformal Ward identities that combines all the superconformal currents and the associated parameters in one multiplet is given for theories with rigid N = 1 or N = 2 supersymmetry. This form of the Ward identities is applied to the spontaneously broken N = 2 Yang-Mills theory and used to derive a condition on the low energy effective action. This condition is satisfied by the solution proposed by Seiberg and Witten.

Operator product expansions in four-dimensional superconformal field theories

Abstract The operator product expansion in four-dimensional superconformal field theory is discussed. It is demonstrated that the OPE takes a particularly simple form for certain classes of operators. These are chiral operators, principally of interest in theories with N = 1 or N = 2 supersymmetry, and analytic operators, of interest in N = 2 and N = 4. It is argued that the Greens functions of such operators can be determined up to constants.

N=2 superconformal models, Landau-Ginsburg hamiltonians and the ϵ expansion

Abstract The anomalous dimensions of a class of operators, operator product expansions and the central change, c , are calculated in a family of N =2 supersymmetric two-dimensional Landau-Ginsburg models. The results allow the identification of these theories with N =2 minimal superconformal models. A key role is played by the N =2 non-renormalization theorem.