D.M. Capper

Regularization by dimensional reduction of supersymmetric and non-supersymmetric gauge theories

We apply the technique of dimensional reduction to both supersymmetric and non-supersymmetric theories. Explicit one- and two-loop calculations show that in the latter case the technique is a viable alternative to conventional dimensional regularization, while in the former it preserves the Slavnov-Taylor identities of both supersymmetry and gauge invariance.

The Background Field Method at Two Loops: A General Gauge {Yang-Mills} Calculation

Abstract We calculate the two-loop contribution to the β function of pure Yang-Mills theory in an arbitrary gauge using the background field method. This serves as a further check on the consistency of the method beyond one loop, explicitly verifying Kalloshs theorem, and also clarifies the role of the gauge parameter in this technique.

On the evaluation of integrals in the light-cone gauge

Abstract We consider the evaluation of Feynman integrals in the light-cone gauge. The various prescriptions that can be used to remove the ambiguities arising in this gauge are discussed. As an example we evaluate the one-loop contribution to the gluon self-energy in N = 4 supersymmetry. Only the gluon loop contribution differs from the usual covariant result and this can be shown to involve only one integral peculiar to the light-cone gauge. Dimensional regularization is employed to evaluate this integral using both the principal value prescription and the prescription suggested by Mandelstam.

The background field method for quantum gravity at two loops

Abstract We consider the background field method for quantum gravity beyond one loop. It is pointed out that the ghost-containing and pure-gauge diagrams separately satisfy the relevant Ward identities. We illustrate this by considering the two-loop graviton self-energy calculation. An analogous situation exists for the Yang-Mills theory, the results for which are given in an appendix. In the light of our results we discuss the feasibility of carrying out a calculation to determine whether quantum gravity is two-loop finite.

Spontaneous symmetry breaking and pseudo-Goldstone bosons in supersymmetry theories

It is shown, for a certain class of supersymmetric theories, that if supersymmetry is unbroken in the tree approximation then it remains unbroken when the one-loop quantum corrections are included. The authors use a simple model to illustrate the above theorem and also to demonstrate that at least some of the massless scalars which plague supersymmetry theories are pseudo-Goldstone bosons.

The effective potential in the light-cone gauge and supersymmetric Yang-Mills theories

Abstract We evaluate the one-loop effective potential, V1, in the light-cone gauge for a general gauge theory with arbitrary scalar and fermion representations. In the case of a general N = 1 supersymmetric gauge theory the result for V1 is simpler than in the Landau gauge; the form of STrM4 is particularly elegant, and in one-loop finite theories we find STrM4 = 0. We show how the renormalisation group relates STrM4 to the scalar anomalous dimension, γ, and we give an explicit calculation of γ in the light-cone gauge.

On the one-loop finiteness of quantum gravity off mass-shell

Abstract We calculate the one-loop counter terms in quantum gravity for a two-parameter gauge using the background field technique. Gauges can be found in which the off-shell counter terms vanish and our results agree with those of Kallosh, Tarasov and Tyutin, who use a somewhat different approach. We discuss the relative merits of the two methods.

Non-transversality of the Yang-Mills self-energy in the planar gauge

Abstract It is shown that the Yang-Mills self-energy in the planar gauge is non-transverse, even though this self-energy satisfies the appropriate Ward identity. The non-transversality implies that the one-loop counterterm is no longer proportional to ( F μν a ) 2 .

A general gauge calculation of the graviton self-energy

Abstract The one-loop graviton contribution to the graviton self-energy is calculated in a general gauge. The Slavnov identities are shown to be satisfied. It is found to be impossible to choose the gauge parameter such that the counterterms are generally covariant.

The Light-Cone Gauge at Two Loops: The Scalar Anomalous Dimension

We demonstrate that the light-cone gauge is a feasible tool for multi-loop computations by using it to evaluate the two-loop scalar anomalous dimension, γ(2), in a general gauge theory. In the special case of supersymmetry we obtain agreement with previous results which were derived using non-light-cone techniques.