P.K. Townsend

Antisymmetric tensor gauge theories and non-linear σ-models

Antisymmetric tensor fields Bμν subject to the gauge transformation δBμν = ϖμξν − ϖνξμ can describe spinless particles. We investigate the properties of field theories with a “non-abelian generalization” of this invariance. One class of such theories is equivalent to non-linear principal chiral σ-models, another to massive Yang-Mills theories. A supersymmetric analogue in 2 + 2 superspace is constructed and leads to the supersymmetric σ-model defined on a general riemannian manifold.

N=3 supersymmetry multiplets with vanishing trace anomaly: Building blocks of the N>3 supergravities

Abstract N ⩾3 supergravity theories with vanishing one-loop trace anomaly may be constructed fron three basic N =3 multiplets, one of which contains an antisymmetric tensor gauge field. As an example we construct the N =4 theory and discuss its relationship to ten-dimensional supergravity.

Covariant quantization of antisymmetric tensor gauge fields

Abstract Covariant quantization of the antisymmetric tensor field Bμν with gauge transformation δBμν=δμξν−δνξμ reveals two unusual features. Firstly, one mode in the covariant Bμν propagator is not cancelled by a Faddeev-Popov ghost but instead decouples by itself as a consequence of Ward identities. This is analogous to the spin 3 2 field ψμ. Secondly, the Faddeev-Popov ghost lagrangian is itself gauge invariant and requires further commuting ghosts for its covariant quantization. These features are exhibited by a diagrammatic analysis of unitarity.

Three-loop finiteness of the N = 4 supersymmetric non-linear σ model

Abstract We formulate the N = 4 supersymmetric non-linear σ model (in two spacetime dimensions) in terms of N = 1 four-dimensional superfields, and give the explicit form of all supersymmetry transformations. Using supergraph techniques we show that all divergent contributions to the two-point function vanish up to the three-loop level. We also show finiteness to leading order in the 1 n expansion.

Anomalies and supersymmetric regularization by dimensio nal reduction

Abstract We show that the superconformal anomalies of super Yang-Mills theory may be correctly calculated using the supersymmetry preserving dimensional regularization by dimensional reduction.

Higher Rank Representations of Lower Spin

Abstract New examples for spins 0, 1 and 1 2 are given of lower spin systems as gauge theories of higher rank fields. These are characterized by the interchange of rank of potentials and field strengths with respect to ordinary gauge theories. The spin-1 action is of fourth time derivative order but ghost-free. A self-coupled supersymmetric theory of this type is also constructed. Couplings to gravity are, however, inconsistent.

The U(1) problem and the Higgs mechanism in two and four dimensions

Abstract The bosonized Schwinger model and the two-dimensional Stueckelberg model are shown to be equivalent, and both are generalized to four dimensions via the topological gauge field A μνϱ . The resolution of the U(1) problem in the former and the Higgs mechanism in the latter are closely related; in covariant gauges they imply the decoupling of “dual” Kogut-Susskind dipoles.

The vanishing volume of N = 1 superspace

Abstract We show that the supergeometry of the new minimal formulation of N = 1 supergravity is a limiting case of the non-minimal supergeometry for which the volume of superspace vanishes. The action for supergravity in this case is then no longer the superdeterminant of the vielbein but is analogous to a special form of the Fayet-Iliopoulos term allowed only for the new minimal supergeometry. We discuss the restrictions on matter couplings imposed by the new and non-minimal supergeometries.

Gauge invariance for spin-1/2

Abstract We construct a lagrangian for an antisymmetric tensor spinor field χ μν , invariant under the gauge transformation δχ μν = (∂ μ γ ν − ∂ ν γ μ )ɛ, and show that it is equivalent to the massless Dirac lagrangian. This is analogous to the description of spin-0 by an antisymmetric tensor field.

Symmetry restoration and gauge field dynamics in the CPn−1 model

Abstract The CPn−1 model has a local U(1) phase invariance for which the gauge field is composite. We show that the generation of dynamics for this field (as occurs in the 1 N expansion) is a consequence of the restoration of the local U(1) symmetry.