Superbranes and Superembeddings

TL;DR

This paper reviews the geometrical superembedding approach to describing super-p-branes, unifying different formulations and clarifying the geometric meaning of symmetries, with applications to M2 and M5-branes.

Contribution

It provides a comprehensive review of the superembedding method, connecting it with existing formulations and extending it to M-branes with detailed geometrical insights.

Findings

Unified description of super-branes and superembeddings.

Clarified geometric origin of kappa-symmetry.

Applied superembedding to M2 and M5-branes.

Abstract

We review the geometrical approach to the description of the dynamics of super-p-branes, Dirichlet branes and the M5-brane, which is based on a generalization of the elements of surface theory to the description of the embedding of supersurfaces into target superspaces. Being manifestly supersymmetric in both, the superworldvolume of the brane and the target superspace, this approach unifies the Neveu-Schwarz-Ramond and the Green-Schwarz formulation and provides the fermionic kappa-symmetry of the Green-Schwarz-type superbrane actions with a clear geometrical meaning of standard worldvolume local supersymmetry. We describe the properties of doubly supersymmetric (superembedding) brane actions and show how they are related to the standard Green-Schwarz formulation. In the second part of the article basic geometrical grounds of the (super)embedding approach are considered and applied to the description of the M2-brane and the M5-brane. Various applications of the superembedding approach are reviewed.