Lattice simulations with exact supersymmetry give central charges and a scaling dimension matching ADE minimal model predictions, supporting the Landau-Ginzburg to superconformal field theory correspondence.
Nicolai mapping vs. exact chiral symmetry on the lattice
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abstract
Two-dimensional N=2 Wess-Zumino model is constructed on the lattice through Nicolai mapping with Ginsparg-Wilson fermion. The Nicolai mapping requires a certain would-be surface term in the bosonic action which ensures the vacuum energy cancellation even on the lattice, but inevitably breaks chiral symmetry. With the Ginsparg-Wilson fermion, the holomorphic structure of the would-be surface term is maintained, leaving a discrete subgroup of the exact chiral symmetry intact for a monomial scalar potential. By this feature both boson and fermion can be kept massless on the lattice without any fine-tuning.
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Numerical study of ADE-type $\mathcal{N}=2$ Landau--Ginzburg models
Lattice simulations with exact supersymmetry give central charges and a scaling dimension matching ADE minimal model predictions, supporting the Landau-Ginzburg to superconformal field theory correspondence.