Ultra-violet Finiteness in Noncommutative Supersymmetric Theories

We consider the ultra-violet divergence structure of general noncommutative supersymmetric $U(N_c)$ gauge theories, and seek theories which are all-orders finite.Comment: 11 pages, Tex, one figure. Uses harvmac (big) and eps

Fayet-Iliopoulos D-terms and anomaly mediated supersymmetry breaking

We show that in a minimal extension of the MSSM by means of an extra U(1) gauge group, the negative mass-squared problem characteristic of the Anomaly Mediated Supersymmetry Breaking scenario is naturally solved by means of Fayet-Iliopoulos D-terms. We derive a set of sum rules for the sparticle masses which are consequences of the resulting framework.Comment: 11 pages, including 1 figure. Plain TeX. Uses Harvmac and epsf. Final version to appear in Phys. Lett. B; some minor improvement

The Exact Tachyon Beta-Function for the Wess-Zumino-Witten Model

We derive an exact expression for the tachyon $\beta$-function for the Wess-Zumino-Witten model. We check our result up to three loops by calculating the three-loop tachyon $\beta$-function for a general non-linear $\sigma$-model with torsion, and then specialising to the case of the WZW model.Comment: 13pp, uses harvmac (with figures appended as a a standard PostScript file), LTH 31

The Gaugino \beta-Function

We present an elegant exact formula for the gaugino $\beta$-function in a softly-broken supersymmetric gauge theory, of the form $\beta_M = {\cal O}(\beta_g/g)$, where $\beta_g$ is the gauge $\beta$ function and ${\cal O}$ is a simple differential operator acting on the gauge coupling $g$ and the Yukawa coupling.Comment: 11 pages, tex, no figures. Uses harvmac. Minor error in derivation of Eq. (14) correcte

Quasi-infra-red fixed points and renormalisation group invariant trajectories for non-holomorphic soft supersymmetry breaking

In the MSSM the quasi-infra-red fixed point for the top-quark Yukawa coupling gives rise to specific predictions for the soft-breaking parameters. We discuss the extent to which these predictions are modified by the introduction of additional ``non-holomorphic'' soft-breaking terms. We also show that in a specific class of theories there exists an RG-invariant trajectory for the ``non-holomorphic'' terms, which can be understood using a holomorphic spurion term.Comment: 24 pages, TeX, two figures. Uses Harvmac (big) and epsf. Minor errors corrected, and the RG trajectory explained in terms of a holomorphic spurion ter

Six-loop divergences in the supersymmetric Kahler sigma model

The two-dimensional supersymmetric \s-model on a K\"ahler manifold has a non-vanishing \b-function at four loops, but the \b-function at five loops can be made to vanish by a specific choice of renormalisation scheme. We investigate whether this phenomenon persists at six loops, and conclude that it does not; there is a non-vanishing six-loop \b-function irrespective of renormalisation scheme ambiguities.Comment: 13pp, uses phyzzx, LTH 287 (published in Int. J. Mod. Phys. A

Quantum Non-abelian Toda Field Theories

We derive an explicit, exactly conformally invariant form for the action for the non-abelian Toda field theory. We demonstrate that the conformal invariance conditions, expressed in terms of the $\beta$-functions of the theory, are satisfied to all orders, and we use our results to obtain a value for the central charge agreeing with previous calculations.Comment: 28pp, harvmac (choose "b" option

One-loop renormalisation of general N=1/2 supersymmetric gauge theory

We investigate the one-loop renormalisability of a general N=1/2 supersymmetric gauge theory coupled to chiral matter, and show the existence of an N=1/2 supersymmetric SU(N)xU(1) theory which is renormalisable at one loop.Comment: 30 pages, including 8 figures. Plain TeX. Uses Harvmac and eps