Can we change c in four-dimensional CFTs by exactly marginal deformations?

Abstract

There is no known obstructions, but we have not been aware of any concrete examples, either. The Wess-Zumino consistency condition for the conformal anomaly says that a cannot change but does not say anything about c. In supersymmetric models, both a and c are determined from the triangle t’Hooft anomalies and the unitarity demands that both must be fixed, so the unitary supersymmetric conformal field theories do not admit such a possibility. Given this field theory situation, we construct an effective AdS/CFT model without supersymmetry in which c changes under exactly marginal deformations.