Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain
arXiv:1611.02975 · doi:10.3390/sym9010002
Abstract
Diffusion-limited erosion is a distinct universality class of fluctuating interfaces. Although its dynamical exponent , none of the known variants of conformal invariance can act as its dynamical symmetry. In spatial dimensions, its infinite-dimensional dynamic symmetry is constructed and shown to be isomorphic to the direct sum of three loop-Virasoro algebras, with the maximal finite-dimensional sub-algebra . The infinitesimal generators are spatially non-local and use the Riesz-Feller fractional derivative. Co-variant two-time response functions are derived and reproduce the exact solution of diffusion-limited erosion. The relationship with the terrace-step-kind model of vicinal surfaces and the integrable XXZ chain are discussed.
Latex 2e, 28 pp, 4 figures (revised, with 2 new figures)
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