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

## TL;DR

This paper demonstrates that in non-supersymmetric four-dimensional conformal field theories, the central charge c can be altered through exactly marginal deformations, challenging previous assumptions based on supersymmetric models.

## Contribution

The authors construct an effective AdS/CFT model showing that c can change under exactly marginal deformations in non-supersymmetric 4D CFTs, providing a concrete example.

## Key findings

- c can be changed by exactly marginal deformations in non-supersymmetric models
- Supersymmetric theories do not allow c to change due to anomaly constraints
- Constructed an explicit AdS/CFT example demonstrating this possibility

## 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.