Superstrings in higher order extensions of Finsler superspaces

Abstract

The work proposes a general background of the theory of field interactions and strings in spaces with higher order anisotropy. Our approach proceeds by developing the concept of higher order anisotropic superspace which unifies the logical and mathematical aspects of modern Kaluza-Klein theories and generalized Lagrange and Finsler geometry and leads to modelling of physical processes on higher order fiber bundles provided with non-linear and distinguished connections and metric structures. The view adopted here is that a general field theory should incorporate all possible anisotropic and stochastic manifestations of classical and quantum interactions and, in consequence, a corresponding modification of basic principles and mathematical methods in formulation of physical theories. The presentation is divided into two parts. The first five sections cover the higher order anisotropic superspaces. We focus on the geometry distinguished by non-linear connection vector superbundles, consider different supersymmetric extensions of Finsler and Lagrange spaces and analyze the structure of basic geometric objects on such superspaces. The remaining five sections are devoted to the theory of higher order anisotropic superstrings. In the framework of supersymmetric non-linear sigma models in Finsler extended backgrounds we prove that the low-energy dynamics of such strings contains equations of motion for locally anisotropic field interactions. Our work is to be compared with important previous variants of extensions of Finsler geometry and gravity. There are substantial differences, because we rely on modeling of higher order anisotropic interactions on superbundle spaces and do not propose some “exotic” Finsler models but a general approach which for trivial or corresponding parametrization of non-linear connection structures reduces to Kaluza-Klein and other variants of compactified higher-dimension spacetimes. The geometry of non-linear connections (not being confused with connections for non-linear realizations of gauge supergroups) is first considered for superspaces and possible consequences on non-linear connection fields for compatible propagations of strings in anisotropic backgrounds are analyzed. Finally, we note that the developed computation methods are general (in some aspects very similar to those for Einstein-Cartan-Weyl spaces which is a priority comparing with other cumbersome calculations in Finsler geometry) and admit extensions to various Clifford and spinor bundles.