Renormalisation Group Flows and Conserved Vector Currents

TL;DR

This paper demonstrates the irreversibility of renormalization group flows in two dimensions using conserved vector currents, introducing a quantity that decreases along the flow and is stationary at fixed points, with extensions to higher dimensions.

Contribution

It introduces a new method to show RG flow irreversibility via conserved currents and extends the analysis to higher dimensions using spectral decomposition.

Findings

A quantity decreasing along RG flows in 2D models.

Stationary at fixed points, matching the affine Lie algebra level.

Extensions of the method to higher-dimensional theories.

Abstract

Irreversibility of RG flows in two dimensions is shown using conserved vector currents. Out of a conserved vector current, a quantity decreasing along the RG flow is built up such that it is stationary at fixed points where it coincides with the constant coefficient of the two current correlation function. For Wess-Zumino-Novikov-Witten models this constant coefficient is the level of their associated affine Lie algebra. Extensions to higher dimensions using the spectral decomposition of the two current correlation function are studied.