A perturbative re-analysis of N=4 supersymmetric Yang--Mills theory

Abstract

The finiteness properties of the N=4 supersymmetric Yang-Mills theory are reanalyzed both in the component formulation and using N=1 superfields, in order to discuss some subtleties that emerge in the computation of gauge dependent quantities. The one-loop corrections to various Green functions of elementary fields are calculated. In the component formulation it is shown that the choice of the Wess-Zumino gauge, that is standard in supersymmetric gauge theories, introduces ultraviolet divergences in the propagators at the one-loop level. Such divergences are exactly cancelled when the contributions of the fields that are put to zero in the Wess-Zumino gauge are taken into account. In the description in terms of N=1 superfields infrared divergences are found for every choice of gauge different from the supersymmetric generalization of the Fermi-Feynman gauge. Two-, three- and four-point functions of N=1 superfields are computed and some general features of the infrared problem are discussed. We also examine the effect of the introduction of mass terms for the (anti) chiral superfields in the theory, which break supersymmetry from N=4 to N=1. It is shown that in the mass deformed model no ultraviolet divergences appear in two-point functions. It argued that this result can be generalized to n-point functions, supporting the proposal of a possible of use of this modified model as a supersymmetry-preserving regularization scheme for N=1 theories.

41 pages, LaTeX2e, uses feynMP package to draw Feynman diagrams

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• The Operator Product Expansion of N=4 SYM and the 4-point Functions of Supergravity
• On form factors in N=4 sym
• Quarter BPS Operators in N=4 SYM
• Background field calculations and nonrenormalization theorems in 4d supersymmetric gauge theories and their low-dimensional descendants
• BPS Wilson loops in generic conformal N=2 SU(N) SYM theories
• Correlators of Short Multi-Trace Operators in N=4 Supersymmetric Yang-Mills
• Integrability in N=2 superconformal gauge theories
• N=4 supersymmetric Yang-Mills theory and the AdS/SCFT correspondence
• The Bremsstrahlung function of $\mathcal{N}=2$ SCQCD
• N=1* model and glueball superpotential from Renormalization-Group-improved perturbation theory
• Quantum superfield supersymmetry
• N=1* model superpotential revisited (IR behaviour of N=4 limit)
• Wilson loops as defects in N=2 conformal field theories
• Matrix Model and beta-deformed N=4 SYM