Quantum conformal algebras and closed conformal field theory

Abstract

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 ⊤. The OPE structure is uniquely determined by two central charges, c and a, where c has a direct interpretation as the central extension of the algebra, while the combination 1 − a c is a structure constant. When the ratio c a is different from 1, the multiplet ⊤ contains the stress-tensor, 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. ⊤ mixes with a second multiplet ⊤ ∗ 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 ⊤ contains just the stress-tensor.