Penrose Transform on D-Modules, Moduli Spaces and Field Theory

Francisco Bulnes

Department of Research in Mathematics and Engineering, Technological Institute of High Studies of Chalco, Chalco, Mexico.

DOI: 10.4236/apm.2012.26057                

Abstract

We consider a generalization of the Radon-Schmid transform on coherent D-modules of sheaves of holomorphic complex bundles inside a moduli space, with the purpose of establishing the equivalences among geometric objects (vector bundles) and algebraic objects as they are the coherent D-modules, these last with the goal of obtaining conformal classes of connections of the holomorphic complex bundles. The class of these equivalences conforms a moduli space on coherent sheaves that define solutions in field theory. Also by this way, and using one generalization of the Penrose transform in the context of coherent D-modules we find conformal classes of the space-time that include the heterotic strings and branes geometry.

Keywords

Penrose Transform; Coherent D-Modules; Derived Sheaf; Moduli Space; Conformal Classes; Heterotic Strings

Conflicts of Interest

The authors declare no conflicts of interest.

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