O. Gamayun

M. Gritskov

A. Losev

A new algebraic method shows beta functions arise when conformal symmetry breaks, reproducing Cardy’s formula without computing correlators.

We propose a new algebraic way to understand how perturbations break conformal symmetry. Instead of computing complicated correlation functions, the beta function emerges as an obstruction to consistently deforming the symmetry algebra. Applied to two-dimensional theories with current-current deformations, the method reproduces Cardy’s formula for the leading beta function and could simplify higher-order calculations. 

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 conformal algebra 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.

Cohomological beta function