The effective Maxwell-Chern-Simons theory for FQH excitations admits a non-perturbative unitary SDiff-equivariant construction that is nevertheless non-differentiable.
Pickrell, On the Action of the Group of Diffeomor- phisms of a Surface on Sections of the Determinant Line Bundle, Pacific Journal of Mathematics193, 177 (2000)
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Non-Perturbative SDiff Covariance of Fractional Quantum Hall Excitations
The effective Maxwell-Chern-Simons theory for FQH excitations admits a non-perturbative unitary SDiff-equivariant construction that is nevertheless non-differentiable.