Cohomological beta function

We propose a cohomological approach to computing the conformal anomaly. Using the example of current-current deformations of two-dimensional conformal field theories, we reproduce the well-known Cardy formula for the leading contribution to the perturbative beta function as the coefficient of the cocycle that realizes the obstruction to deforming the Virasoro module structure on the state space. In addition to offering a novel conceptual perspective on the conformal anomaly, the proposed approach is anticipated to provide an efficient tool for computing higher-order coefficients of perturbative beta functions.