Superspace Measures, Invariant Actions, and Component Projection Formulae for (2,2) Supergravity

In the framework of the prepotential description of superspace two-dimensional $(2,2)$ supergravity, we discuss the construction of invariant integrals. In addition to the full superspace measure, we derive the measure for chiral superspace, and obtain the explicit expressions for going from superspace actions to component actions. We consider both the minimal $U_A(1)$ and the extended $U_V(1) \otimes U_A(1)$ theories.Comment: 22 pages, Late

Prepotentials for (2,2) Supergravity

We present a complete solution of the constraints for two-dimensional, N=2 supergravity in N=2 superspace. We obtain explicit expressions for the covariant derivatives in terms of the vector superfield $H^m$ and, for the two versions of minimal (2,2) supergravity, a chiral or twisted chiral scalar superfield $\phi$.Comment: 16 pages, BRX-TH-36

Holomorphy, Minimal Homotopy and the 4D, N = 1 Supersymmetric Bardeen-Gross-Jackiw Anomaly

By use of a special homotopy operator, we present an explicit, closed-form and simple expression for the left-right Bardeen-Gross-Jackiw anomalies described as the proper superspace integral of a superfunction.Comment: 16 pp, LaTeX, Replacement includes addition comment on WZNW term and one new referenc

Noncommutative Supersymmetric Gauge Anomaly

We extend the general method of hep-th/0009192 to compute the consistent gauge anomaly for noncommutative 4d SSYM coupled to chiral matter. The choice of the minimal homotopy path allows us to obtain a simple and compact result. We perform the reduction to components in the WZ gauge proving that our result contains, as lowest component, the bosonic chiral anomaly for noncommutative YM theories recently obtained in literature.Comment: 14 pages, plain Latex, no figure

Non(anti)commutative SYM theory: Renormalization in superspace

We present a systematic investigation of one-loop renormalizability for nonanticommutative N=1/2, U(N) SYM theory in superspace. We first discuss classical gauge invariance of the pure gauge theory and show that in contradistinction to the ordinary anticommutative case, different representations of supercovariant derivatives and field strengths do not lead to equivalent descriptions of the theory. Subsequently we develop background field methods which allow us to compute a manifestly covariant gauge effective action. One-loop evaluation of divergent contributions reveals that the theory simply obtained from the ordinary one by trading products for star products is not renormalizable. In the case of SYM with no matter we present a N=1/2 improved action which we show to be one-loop renormalizable and which is perfectly compatible with the algebraic structure of the star product. For this action we compute the beta functions. A brief discussion on the inclusion of chiral matter is also presented.Comment: Latex file, 59 pages, 10 figures, One reference adde

Nonanticommutative superspace and N= 1/2 WZ model

In these proceedings we review the main results concerning superspace geometries with nonanticommutative spinorial variables and field theories formulated on them. In particular, we report on the quantum properties of the WZ model formulated in the N=1/2 nonanticommutative superspace.Comment: 9 pages, plain Latex, contribution to the proceedings of the Copenhagen RTN workshop, 15-20 September 200

Two-loop Renormalization for Nonanticommutative N=1/2 Supersymmetric WZ Model

We study systematically, through two loops, the divergence structure of the supersymmetric WZ model defined on the N=1/2 nonanticommutative superspace. By introducing a spurion field to represent the supersymmetry breaking term F^3 we are able to perform our calculations using conventional supergraph techniques. Divergent terms proportional to F, F^2 and F^3 are produced (the first two are to be expected on general grounds) but no higher-point divergences are found. By adding ab initio F and F^2 terms to the original lagrangian we render the model renormalizable. We determine the renormalization constants and beta functions through two loops, thus making it possible to study the renormalization group flow of the nonanticommutation parameter.Comment: 36 pages, 25 figures, Latex fil