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

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

N=1N=1 supersymmetry and the three loop gauge beta function

We calculate the three loop gauge $\beta$-function for an abelian $N=1$ supersymmetric gauge theory, using DRED. We construct a coupling constant redefinition that relates the result to the corresponding term in the NSVZ $\beta$-function, and by generalising this redefinition to the non-abelian case we derive the DRED three loop gauge $\beta$-function for the non-abelian case.Comment: 6 pages. Uses Harvmac. Minor referencing error and typos 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