TITLE:
Penrose Transform on Induced DG/H-Modules and Their Moduli Stacks in the Field Theory
AUTHORS:
Francisco Bulnes
KEYWORDS:
Penrose Transform; Coherent G-Quasi-Equivariant D-Modules; Hecke Sheaf; Moduli Stacks; Moduli Spaces
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.3 No.2,
March
5,
2013
ABSTRACT: We consider generalizations of the Radon-Schmid transform on coherent DG/H-Modules, with the intention of obtaining the equivalence between geometric objects (vector bundles) and algebraic objects (D-Modules) characterizing conformal classes in the space-time that determine a space moduli [1] on coherent sheaves for the securing solutions in field theory [2]. In a major context, elements of derived categories like D-branes and heterotic strings are considered, and using the geometric Langlands program, a moduli space is obtained of equivalence between certain geometrical pictures (non-conformal world sheets [3]) and physical stacks (derived sheaves), that establishes equivalence between certain theories of super symmetries of field of a Penrose transform that generalizes the implications given by the Langlands program. With it we obtain extensions of a cohomology of integrals for a major class of field equations to corresponding Hecke category.