Scaling functions from q-deformed Virasoro characters

TL;DR

This paper introduces a new RG scaling function derived from q-deformed Virasoro characters, capable of describing flows between various conformal field theories, including supersymmetric ones, and constructing particle spectra with unstable pseudo-particles.

Contribution

It presents a novel RG scaling function based on q-deformed Virasoro characters, enabling analysis of flows between different conformal field theories and particle spectrum construction.

Findings

The new functions match information from massive theory approaches.

They allow RG flows between different series of conformal theories.

They facilitate the construction of particle spectra with unstable pseudo-particles.

Abstract

We propose a renormalization group scaling function which is constructed from q-deformed fermionic versions of Virasoro characters. By comparison with alternative methods, which take their starting point in the massive theories, we demonstrate that these new functions contain qualitatively the same information. We show that these functions allow for RG-flows not only amongst members of a particular series of conformal field theories, but also between different series such as N=0,1,2 supersymmetric conformal field theories. We provide a detailed analysis of how Weyl characters may be utilized in order to solve various recurrence relations emerging at the fixed points of these flows. The q-deformed Virasoro characters allow furthermore for the construction of particle spectra, which involve unstable pseudo-particles.