Penrose Transform on Induced DG=H-Modules and Their Moduli Stacks in the Field Theory II

Abstract

We look at generalizations of the Radon-Schmid transform on coherent DG=H -Modules with the aim of obtaining equivalence between geometric objects (vector bundles) and algebraic objects (D-Modules) that characterize conformal groups in the space-time that determine a moduli space on coherent sheaves for the purpose of obtaining solutions in field theory. Elements of derived categories such as D-branes and heterotic strings are regarded in a significant sense. Similarly, a moduli space is obtained for equivalence between some geometrical pictures (non-conformal worldsheets) and physical stacks using the geometric Langlands programme (derived sheaves). This provides equivalences between several theories of field supersymmetries of a Penrose transform that generalises the Langlands program’s implications. Extensions of a cohomology of integrals for a major class of field equations to the corresponding Hecke group are obtained with it.