Superbranes and Generic Target Space Curving

TL;DR

This paper explores embedding superbranes into curved target spaces, proposing a covariant formulation using infinite-component spinors and a Dirac-like equation, extending the traditional finite-component approach.

Contribution

It introduces a new covariant superbrane formulation in generic curved spaces using infinite-component spinors and a Dirac-like equation, overcoming limitations of finite-component spinor methods.

Findings

Finite-component spinor superbrane formulation limited to restricted curving.

Infinite-component spinors enable fully covariant superbrane embedding.

A Dirac-like equation facilitates manifest covariance in curved target spaces.

Abstract

Embedding of a Green-Schwarz superbrane into a generic curved target space in a general covariant way is considered. It is demonstrated explicitely, that the customary superbrane formulation based on finite-component spinors extends to a superspaces of restricted curving only, with the General Coordinate Transformations realized nonlinearly over its orthogonal type subgroups. Infinite-component, world, spinors and a recently constructed corresponding Dirac-like equation, enable a possibility of a manifestly covariant generic curved target space superbrane formulation.