Shrinking fermionic modes, on the lattice and in the continuum

Abstract

Recent lattice data indicates that volume occupied by topological fermionic modes shrinks to zero in the continuum limit of vanishing lattice spacing. The data apparently cannot be accommodated within, say, conventional instanton model. We review field-theoretic arguments which demonstrate that the topological fermionic modes are to shrink to a vanishing submanifold of the whole four dimensional space provided that measurements are performed with high resolution. Moreover, the data fit well the emerging overall picture of lower-dimensional defects in the Euclidean vacuum of Yang-Mills theories. We also mention results on localization of scalar particles.