Fractal Index, Central Charge and Fractons

We introduce the notion of fractal index associated with the universal class h of particles or quasiparticles, termed fractons which obey specific fractal statistics. A connection between fractons and conformal field theory (CFT)-quasiparticles is established taking into account the central charge c[ν] and the particle-hole duality ν<-->1/ν, for integer-value ν of the statistical parameter. In this way, we derive the Fermi velocity in terms of the central charge as v ~(c[ν ])/(ν +1). The Hausdorff dimension h which labeled the universal classes of particles and the conformal anomaly are therefore related. Following another route, we also established a connection between Rogers dilogarithm function, Farey series of rational numbers and the Hausdorff dimension.