Fractal index, central charge and fractons

Details Fractal index, central charge and fractons Fractal index, central charge and fractons

2000-02-22

arxiv.org/abs/hep-th/0002181v9

Mod.Phys.Lett. A15 (2000) 1931-1940

Physics

High Energy Physics

High Energy Physics - Theory

latex, 12 pages, To appear in Mod. Phys. Lett. A (2000)

Scientific paper

10.1142/S0217732300002206

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 $c[\nu]$ and the particle-hole duality $\nu\longleftrightarrow\frac{1}{\nu}$, for integer-value $\nu$ of the statistical parameter. In this way, we derive the Fermi velocity in terms of the central charge as $v\sim\frac{c[\nu]}{\nu+1}$. The Hausdorff dimension $h$ 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.

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