C-theorem for two dimensional chiral theories

TL;DR

This paper extends the $C$-theorem to two-dimensional chiral theories by introducing two monotonic $C$-functions whose difference relates to anomaly matching conditions.

Contribution

It proposes a novel extension of the $C$-theorem to chiral theories, revealing a constant difference linked to anomalies.

Findings

Two monotonic $C$-functions are introduced.

The difference between these functions is a RG flow constant.

This constant reproduces 't Hooft anomaly matching conditions.

Abstract

We discuss an extension of the $C$-theorem to chiral theories. We show that two monotonically decreasing $C$-functions can be introduced. However, their difference is a constant of the renormalization group flow. This constant reproduces the 't Hooft anomaly matching conditions.