Quantum Conformal Algebras and Closed Conformal Field Theory

TL;DR

This paper introduces a new class of conformal field theories characterized by a closed quantum conformal algebra, providing insights into strongly coupled supersymmetric gauge theories and their operator structures.

Contribution

It proposes the concept of closed quantum conformal algebras as exact solutions for strongly coupled large-N_c gauge theories, extending the understanding of operator product expansions.

Findings

Identification of a novel class of conformal field theories with closed algebra

Operator product expansion of the conserved current multiplet T determined by two central charges

Distinct c/a ratio indicating richer structure beyond N=4 superconformal theories

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 conjecture 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 T. The OPE structure is uniquely determined by two central charges, c and a. The multiplet T does not contain just the stress-tensor, but also R-currents and finite mass operators. For this reason, the ratio c/a is different from 1. 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. T 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.