GENERAL BOSONIC SIGMA-MODELS AND STRING EFFECTIVE ACTIONS

The renormalization of general bosonic two dimensional σ models including torsion and allowing for the definition of finite local dimension 2 composite operators and their products is carefully discussed. This framework allows an extension of the Curci-Paffuti relation to be simply derived and also shows how the conditions for the vanishing of the trace of the energy momentum tensor may be derived from an action to all orders of perturbation theory. This derivation of an action for the massless modes of the closed bosonic string is related to Zamolodchikov's c-theorem. Detailed calculations are undertaken to two loops and the action then constructed is verified to coincide with a special case of previous treatments. The analysis is based on dimensional regularisation. Special attention is payed to the treatment of the anti-symmetric ε{lunate}μν tensor. The main discussion assumes that the d-dimensional regularising space posesses an almost complex structure, although an alternative treatment with ε{lunate}μν regarded as restricted to just two dimensions is also considered. The renormalised action for the σ model is shown to be compatible with the preservation of gauge invariance when the original action includes gauge fields and satisfies an appropriate gauge symmetry. The general analysis is applied to the special case of the σ model with fields on squashed S3. © 1990.