Quantum conformal algebras and closed conformal field theory

We investigate the quantum conformal algebras of N = 2 and N = 1 supersymmetric gauge theories. Phenomena occurring at strong coupling are analysed using the Nachtmann theorem and very general, model-independent, arguments. The results lead us to introduce a novel class of conformal field theories, identified by a closed quantum conformal algebra. We argue that they are the exact solution to the strongly coupled large-N-c, limit of the open conformal field theories. We study the basic properties of closed conformal field theory and work out the operator product expansion of the conserved current multiplet I. The OPE structure is uniquely determined by two central charges, c acid a, where c has a direct interpretation as the central extension of the algebra, while the combination 1 - ale is a structure constant. When the ratio cia is different from 1, the multiplet I contains the stress-tenser, R-currents and finite mass operators. On the other hand, an open algebra contains an infinite tower of non-conserved currents, organized in pairs and singlets with respect to renormalization mixing. I mixes with a second multiplet T* and the main consequence is that c and a have different subleading corrections, The closed algebra simplifies considerably at c = a, where it coincides with the N = 4 one and I contains just the stress-tenser. (C) 1999 Elsevier Science B.V, All rights reserved.