c-Theorem for Disordered Systems

TL;DR

This paper introduces a new parameter b in disordered 2D systems that behaves like a c-theorem analog, relating to the algebraic structure and free energy, with potential applications to Dirac fermions with randomness.

Contribution

It proposes a novel flow parameter b for disordered systems, linking it to algebraic structures and free energy, extending the concept of the c-theorem.

Findings

b relates to the algebraic central extension and free energy

b's flow along RG trajectories is analogous to the c-theorem

Application to Dirac fermions with random gauge potential

Abstract

We find an analog of Zamolodchikov's c-theorem for disordered two dimensional noninteracting systems in their supersymmetric representation. For this purpose we introduce a new parameter b which flows along the renormalization group trajectories much like the central charge for unitary two dimensional field theories. However, it is not known yet if this flow is irreversible. b turns out to be related to the central extension of a certain algebra, a generalization of the Virasoro algebra, which we show may be present at the critical points of these theories. b is also related to the physical free energy of the disordered system defined on a cylinder. We discuss possible applications by computing b for two dimensional Dirac fermions with random gauge potential.