Dimensional reducers: Parisi-Sourlas super-rotations as BRST transformations

Abstract

BRST cohomology is shown to imply Parisi-Sourlas dimensional reduction in Minkowski space. Supersymmetric rotations into lightlike vectors are shown to be BRST transformations. The author calculates their cohomology and thus gives a non-perturbative demonstration of dimensional reduction in Minkowski space. It is shown how the BRST operator and its cohomology in the second quantised 'field' theory follows from the BRST operator in the first quantised 'particle' theory.