Koszul-Tate Cohomology as Lowest-Energy Modules of Non-Centrally Extended Diffeomorphism Algebras

Abstract

Fock modules for multi-dimensional Virasoro algebras (non-central extensions of the diffeomorphism algebra vect(N)) have recently been reported. Using ideas from the antifield formalism, I construct new classes of lowest-energy modules, as cohomology groups of a certain Fock complex. The Fock construction involves a passage to p-jets prior to normal ordering, but the abelian charges usually diverge in the limit p --> oo. The requirement of a finite limit imposes severe restrictions on the number of spacetime dimensions and on the order of the Euler-Lagrange (EL) equations. Under some natural assuptions (the EL equations are first order for fermions and second order for bosons, and no reducible gauge symmetries appear), finiteness is only possible when the number of spacetime dimensions N = 4.