Diffusion-limited erosion (DLE) is a paradigmatic member of a specific universality class of fluctuating interfaces, distinct from the familiar Edwards-Wilkinson and Kardar-Parisi-Zhang universality classes. Other members in this class include the terrace-step-kind model of vicinal surfaces and also the integrable XXZ chain, conditioned to large values of the stationary current.

Although the dynamical exponent of DLE is z=1, none of the known variants of conformal invariance can act as its dynamical symmetry. In d=1 spatial dimensions, the infinite-dimensional dynamic symmetry algebra of DLE is constructed explicitly and will be shown to be isomorphic to the direct sum of three loop-Virasoro algebras. 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.

[1] M. Henkel, J. Phys. A 49, 49LT02 (2016) [arxiv:1606.06207]

[2] M. Henkel, submitted to Symmetry, [arxiv:1611.02975]