Renormalisation of the Fayet-Iliopoulos D-term

We consider the renormalisation of the Fayet-Iliopoulos D-term in a softly-broken Abelian supersymmetric theory. We show that there exists (at least through three loops) a renormalisation group invariant trajectory for the coefficient of the D-term, corresponding to the conformal anomaly solution for the soft masses and couplings.Comment: 11 pages, TeX, Uses Harvmac (big). References added, minor corrections (including a sign error for the zeta(3) terms), and discussion of scheme dependence corrected and amplifie

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

We show that N=1/2 supersymmetric gauge theory is renormalisable at one loop, but only after gauge invariance is restored in a non-trivial fashion.Comment: 11 pages, including 3 figures. Plain TeX. Uses Harvmac and epsf. Minor changes and reference adde

Clarifying Some Remaining Questions in the Anomaly Puzzle

We discuss several points that may help to clarify some questions that remain about the anomaly puzzle in supersymmetric theories. In particular, we consider a general N=1 supersymmetric Yang-Mills theory. The anomaly puzzle concerns the question of whether there is a consistent way to put the R-current and the stress tensor in a single supercurrent, even though in the classical theory they are in the same supermultiplet. As is well known, the classically conserved supercurrent bifurcates into two supercurrents having different anomalies in the quantum regime. The most interesting result we obtain is an explicit expression for the lowest component of one of the two supercurrents in 4-dimensional spacetime, namely the supercurrent that has the energy-momentum tensor as one of its components. This expression for the lowest component is an energy-dependent linear combination of two chiral currents, which itself does not correspond to a classically conserved chiral current. The lowest component of the other supercurrent, namely, the R-current, satisfies the Adler-Bardeen theorem. The lowest component of the first supercurrent has an anomaly that we show is consistent with the anomaly of the trace of the energy-momentum tensor. Therefore, we conclude that there is no consistent way to put the R-current and the stress tensor in a single supercurrent in the quantized theory. We also discuss and try to clarify some technical points in the derivations of the two-supercurrents in the literature. These latter points concern the significance of infrared contributions to the NSVZ beta-function and the role of the equations of motion in deriving the two supercurrents.Comment: 22 pages, no figure. v2: minor changes. v3: sections re-organized. new subsections (IVA, IVB) added. references adde

Asymptotic Pad\'e Approximants and the SQCD β\beta-function

We present a prediction for the four loop $\beta$-function for SQCD based on the method of Asymptotic Pad\'e Approximants.Comment: 8 pages, including 2 figures. Plain TeX. Uses Harvmac and eps

Infra-red stability of Yukawa and soft-breaking fixed points

We investigate the infra-red stability of the fixed points in the evolution of the Yukawa couplings, $A$-parameters and soft scalar masses in a broad class of supersymmetric theories. We show that the issue of stability is essentially determined in all three cases by the eigenvalues of the same matrix. In a very wide range of physically interesting theories it follows that, in the asymptotically free case, the existence of stable infra-red fixed points for the Yukawa couplings implies stable infra-red fixed points for the $A$-parameters and soft scalar masses.Comment: 12 pages, tex, Uses harvmac (big). Errors corrected in Eqs. (33)-(35), and some references adde

Reduction of Couplings in Quantum Field Theories with applications in Finite Theories and the MSSM

We apply the method of reduction of couplings in a Finite Unified Theory and in the MSSM. The method consists on searching for renormalization group invariant relations among couplings of a renormalizable theory holding to all orders in perturbation theory. It has a remarkable predictive power since, at the unification scale, it leads to relations between gauge and Yukawa couplings in the dimensionless sectors and relations involving the trilinear terms and the Yukawa couplings, as well as a sum rule among the scalar masses and the unified gaugino mass in the soft breaking sector. In both the MSSM and the FUT model we predict the masses of the top and bottom quarks and the light Higgs in remarkable agreement with the experiment. Furthermore we also predict the masses of the other Higgses, as well as the supersymmetric spectrum, both being in very confortable agreement with the LHC bounds on Higgs and supersymmetric particles.Comment: 18 pages, 4 figures. To appear in the proceedings of LT-10, Varna. Based on invited talks given at: LT-10, Varna; PACT-2013, Madrid; SQS'2013, Dubna; CORFU 2013, Corfu, and in several invited seminar

N=1N=1 supersymmetry and the three loop anomalous dimension for the chiral superfield

We calculate the three loop anomalous dimension for a general $N=1$ supersymmetric gauge theory. The result is used to probe the possible existence of renormalisation invariant relationships between the Yukawa and gauge couplings.Comment: 18 pages. Uses Harvmac. Revised version includes discussion of the special case of the Wess-Zumino mode

Large-N supersymmetric beta-functions

We present calculations of the leading and O(1/N) terms in a large-N expansion of the \beta-functions for various supersymmetric theories: a Wess-Zumino model, supersymmetric QED and a non-abelian supersymmetric gauge theory. In all cases N is the number of a class of the chiral superfields in the theory.Comment: 9 pages, tex, five figures. Uses harvmac and epsf. Revised to include a discussion of higher loop DRED ambiguities. Some references added, and notation clarifie

Dimensional Reduction in Non-Supersymmetric Theories

It is shown that regularisation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.Comment: 13 pages, phyzzx, LTH 32

Snowmass Benchmark Points and Three-Loop Running

We present the full three-loop beta-functions for the MSSM generalised to include additional matter multiplets in 5, 10 representations of SU(5). We analyse in detail the effect of three-loop running on the sparticle spectrum for the MSSM Snowmass Benchmark Points. We also consider the effect on these spectra of additional matter multiplets (the semi-perturbative unification scenario).Comment: 28 pages, TeX, 4 figures, 10 tables. Uses Harvmac and eps