# Peculiar* *betas

Quantum field theory

## Peculiarities of beta functions in sigma models

In quantum field theory, beta functions describe the flow of coupling constants, which for sigma models exist as a metric of the target space. Generally, the flow of a metric is expressed by geometric structures. Surprisingly, we find an exception to this in the second order of perturbation theory. The expression we derive has an elegant form in the context of algebraic data, which may be explained by infrared anomalies.