@MISC{Ferreira97revisedversion, author = {P. M. Ferreira and I. Jack and D. R. T. Jones}, title = {Revised Version}, year = {1997} }

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Abstract

We present calculations of the leading and O(1/N) terms in a large-N expansion of the β-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. Feb 1996Coupling constant perturbation theory has constituted the main approach to quantum field theories since their introduction, but it has its limitations. Therefore any approach which reaches beyond it is worthy of attention: one such is large-N expansions, where N denotes the number of fields (or some subset thereof). Simple theories such as O(N)symmetric φ4 have been much studied [1] as has QCD at both large Nc[2] and Nf[3] [4]. In this paper we calculate the β-functions for a Wess-Zumino model, and also for various supersymmetric gauge theories – supersymmetric QED in the limit of large Nf, i.e. for a large number of chiral superfields, together with an abelian gauged Wess-Zumino model and a more general non-abelian theory. In all cases the leading contribution is a simple one-loop calculation, and things become interesting at O(1/N), when bubble sums are involved. It turns out that the supersymmetric D-algebra part of the calculation is