Fractal index, central charge and fractons

We introduce the notion of fractal index associated with the universal clas s h of particles or quasiparticles, termed fractons which obey specific fra ctal statistics. A connection between fractons and conformal field theory ( CFT)-quasiparticles is established taking into account the central charge c [nu] and the particle-hole duality nu <----> 1/nu, for integer-value nu of the statistical parameter. In this way, Ne derive the Fermi velocity in ter ms of the central charge as nu similar to c[nu]/nu +1. The Hausdorff dimens ion h which labeled the universal classes of particles and the conformal an omaly are therefore related. Following another route, we also established a connection between Rogers dilogarithm function, Farey series of rational n umbers and the Hausdorff dimension.