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abstract: 'Disordered 2D chiral fermions provide an effective description of several materials including graphene and topological insulators. While previous analysis considered delta correlated disorder and no ultraviolet cut-offs, we consider here the effect of short range correlated disorder and the presence of a momentum cut-off, providing a more realistic description of condensed matter models. We show that the density of states is anomalous with a critical exponent function of the disorder and that conductivity is universal only when the ultraviolet cut-off is removed, as consequence of the supersymmetric cancellation of the anomalies.'
author:
- Vieri Mastropietro
title: 'Universality, exponents and anomaly cancellation in disordered Dirac fermions'
---

Introduction
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It is known that several materials exhibit fermionic excitations with linear dispersion relation close to the Fermi level, which can be effectively described in terms of $2+1$dimensional Dirac fermions. Early examples include systems displaying integer quantum Hall effect [@LFSG] and [*d-wave superconductors*]{} [@NTW; @ASZ] and more recently [*graphene*]{} [@V3; @H0; @Mi; @CG; @Z1; @FCO] and [*topological insulators*]{} [@N1; @Mo]. In particular, in the case of graphene at half filling it has been observed [@N2] that the [*optical*]{} conductivity (for frequencies greater than the temperature) is essentially constant in a wide 