NONPERTURBATIVE FORMULAS FOR CENTRAL FUNCTIONS OF SUPERSYMMETRIC GAUGE-THEORIES

For quantum held theories that flow between ultraviolet and infrared f ixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories. We develop techniques that allow one to calculate the flows of the central charges and that of t he Euler trace anomaly coefficient in a general N = 1 supersymmetric g auge theory. Exact, explicit formulas for SU(N,) gauge theories in the conformal window are given and analysed. The Euler anomaly coefficien t always satisfies the inequality a(UV) - a(IR) > 0. This is new evide nce in strongly coupled theories that this quantity satisfies a four-d imensional analogue of the c-theorem, supporting the idea of irreversi bility of the RG flow. Various other implications are discussed. (C) 1 998 Elsevier Science B.V.