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

TL;DR

The work investigates whether the four-dimensional Weyl anomaly coefficient $c$ can vary along exactly marginal deformations. A field-theory argument using the local renormalization group shows $a$ cannot depend on marginal couplings, while $c$ is not ruled out, leaving open the possibility of $c$-variation. The authors then provide a concrete non-supersymmetric holographic construction with higher-derivative gravity and a modulus field that yields $c( ext{marginal})$ dependence while keeping $a$ fixed, illustrating that such behavior can arise in an effective AdS/CFT framework. They also discuss unitarity and SUSY-based obstructions, noting that while the holographic model demonstrates feasibility in principle, fully consistent, unitary CFTs (especially non-supersymmetric ones) remain uncertain, with stability concerns for non-SUSY AdS/CFT relevant to the broader viability of these constructions. Overall, the paper reveals a tension between field-theory expectations and gravity realizations, showing that, under fine-tuned holographic conditions, $c$ may vary along exactly marginal deformations, and motivates further scrutiny of conformal data under marginal flows.

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. So, yes, we can.