I was fortunate in that I began research just before what is now perceived to have been a Golden Age for particle physics. The great successes of Quantum Field Theory (QFT) between 1930 and 1960 as a complete description of electromagnetic interactions had been followed by a failure to develop a corresponding framework for the equally important (at the microscopic level) strong, weak and gravitational forces: a failure due to the apparent non-renormalisability (inconsistency) of theories involving vector fields, except for the very simplest one, quantum electrodynamics.
When I started as a graduate student in 1971 the importance of the work of 't Hooft in demonstrating the renormalisability of gauge theories was just beginning to be appreciated. At that time (and this was reflected in the graduate courses I attended) the strong and weak interactions were treated by a number of different, not obviously related, approaches--such as S-matrix theory, and current algebra. I was instinctively drawn to the elegance and simplicity of quantum field theory, which, as it turned out, was to dominate the subsequent development of the subject.
By 1973 there existed well-defined and testable quantum field theories of both the electro-weak interactions (a unified description of electromagnetic and weak phenomena) and the strong interactions. Crucial in the development of these theories was recognition of the importance of a property of quantum field theory known as renormalisation group (RG) invariance. Essentially this property amounts to the fact that the process of renormalising (controlling the infinities in) a field theory leads to the introduction of an arbitrary mass scale, usually denoted μ. In order that physical results be μ-independent, the coupling constants (which control the strength of the particle interactions) must depend on μ, and this dependence is controlled by a calculable function known as the β-function. This function can only be calculated as a power series in the coupling constant, and in 1973 only the leading term of this series was known. For my thesis I calculated the next term; as well as involving complex algebra, this necessitated the development of new techniques in handling integrals (known as Feynman integrals) which arise. These techniques are now a part of every well-equipped theorist's armoury. By 1977 new experiments meant that tests of the strong interaction theory were now sensitive to my calculation.
Since then my research work has mainly dealt with field theoretical aspects of the standard model of elementary particle interactions: for example perturbative quantum chromodynamics, lattice gauge theories, and supersymmetric gauge theories. Specific areas in which I made significant contributions include the following:
For some time I have been involved in a detailed study of the renormalisation properties of supersymmetric gauge theories. The recent work, in particular, opens the way to new and exciting results.
Radiative corrections in supersymmetric theories presents special problems. Many years ago I co-authored an influential paper which described how a modification of dimensional regularisation (dimensional reduction, or DRED) preserves supersymmetry. Ian Jack and I later returned to this topic, and showed that (contrary to a claim made in 1985, and uncontested until our work) there is no obstacle to employment of DRED in non-supersymmetric theories. This is important because for certain calculations in QCD, for example, using DRED is in fact a considerable simplification. Another motivation for it, however, was that it was a necessary preliminary to a calculation of the β-functions for the softly-broken supersymmetric standard model: which is, of course, a non-supersymmetric theory. An obvious application was an extension to two loops of the study of the spectrum of the (conjectured) supersymmetric particles.
An exact relation (the NSVZ relation) between the gauge β-function and the chiral superfield anomalous dimension γ has been known since 1982. This relation has significance in the study of gauge theory duality. In a series of papers, we convincingly demonstrated that a renormalisation scheme satisfying the NSVZ relation can be related perturbatively to the conventional DRED scheme.
We then showed that in a general supersymmetric theory, the β-functions of the soft parameters are related to the evolution of the gauge and Yukawa couplings via a series of exact relations. These exact relations have led to a number of applications.
We demonstrated with our exact results an explicit construction of the coupling constant reduction program of Zimmermann et al, with perturbatively finite theories as a special case. This program is important in the context of our philosophy of infra-red universality. In the standard running analysis, it is assumed that the soft-breaking parameters satisfy a property known as universality at the gauge unification scale. This is necessary to contain flavour changing neutral currents within acceptable bounds. We have shown, however, using a toy model, that in a certain class of theories universality can be strongly infra-red attractive. This is elegant, since in such a theory universality will exist at the gauge unification scale irrespective of the form of the theory at the Planck mass. Remarkably, the particular universal form attained corresponds to that found in certain string--based models. This is an intriguing result, and opens the way for a prediction of the super-particle spectrum with only one arbitrary parameter. A preliminary study of the resulting low energy phenomenology has been performed; but we plan to reassess this in the light of the exact results discussed above. The reasons for the correspondence between our results and expectations based on string theory remain to be explained, and there remains the challenge of constructing a realistic theory.
The exact β-function equations described above also led us to the discovery of a remarkably simple closed form for the soft supersymmetry-breaking terms quite distinct from the normal ``gauge unification universality'' assumption. This solution was independently discovered by Randall and Sundrum in a ``top-down'' approach based on a specific model for the origin of supersymmetry-breaking, and is termed Anomaly Mediated Supersymmetry Breaking (AMSB), because in their scenario the supersymmetry-breaking is transmitted to the observable sector via the conformal anomaly.
We then constructed models based on the MSSM with an extra U(1) symmetry which is used to resolve the AMSB tachyonic slepton problem; one version also featured Yukawa coupling textures to explain the fermion mass hierarchy, and accommodated viable neutrino masses and mixings. We went on to refine the sparticle spectrum predictions for the MSSM and its variants, using the three-loop corrections to the β-functions.
Most recently I have been active in a number of new areas, including multi-Higgs models, N = ½ supersymmetry, flavour physics, and aspects of cosmology. Cosmology is a new and exciting departure for me; we were able to introduce the idea of combining Higgs inflation with supersymmetry. .
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