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arXiv · hep-th/0002181

Fractal index, central charge and fractons

Wellington da Cruz·Rosevaldo de Oliveira
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Abstract

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 $ν\longleftrightarrow\frac{1}ν$, for integer-value $ν$ of the statistical parameter. In this way, we derive the Fermi velocity in terms of the central charge as $v\sim\frac{c[ν]}{ν+1}$. 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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Wellington da Cruz, Rosevaldo de Oliveira. 2000-10-10. Fractal index, central charge and fractons. https://doi.org/10.1142/s0217732300002206

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