Fractal statistics, fractal index and fractons

The concept of fractal index is introduced in connection with the idea of universal class h of particles or quasiparticles termed fractons which obey fractal statistics. We show the relation between fractons and conformal field theory(CFT)-quasiparticles taking into account the central charge c[ν] and the particle-hole duality ν ←→ 1 ν , for integer-value ν of the statistical parameter. The Hausdorff dimension h which labeled the universal classes of particles and the conformal anomaly are therefore related. We also establish a contact between Rogers dilogarithm function, Farey series of rational numbers and the Hausdorff dimension. PACS numbers: 05.30.-d; 05.30.Ch; 05.70.Ce; 75.40.-s