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Fractal index, central charge and fractons
We introduce the notion of fractal index associated with the universal class
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 and the particle-hole duality
, for integer-value of the
statistical parameter. In this way, we derive the Fermi velocity in terms of
the central charge as . The Hausdorff dimension
which labelled 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.Comment: latex, 12 pages, To appear in Mod. Phys. Lett. A (2000
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