Superstrings with boundary fermions

TL;DR

This paper develops a classical framework for open superstrings with boundary fermions representing Chan-Paton factors, aiming towards a fully kappa-symmetric non-abelian D-brane theory, and compares constraints with pure spinor methods.

Contribution

It introduces a boundary geometry with fermionic fibers for superstrings, constrained by kappa-symmetry, and explores its quantisation and relation to non-abelian D-brane actions.

Findings

Boundary geometry described by a bundle with fermionic fibers.

Constraints on non-abelian field strength match pure spinor results.

Develops covariant formalism and discusses quantisation challenges.

Abstract

The Green-Schwarz action for an open superstring with additional boundary fermions, representing Chan-Paton factors, is studied at the classical level. The boundary geometry is described by a bundle, with fermionic fibres, over the super worldvolume of a D-brane together with a map from the total space into the type II target superspace. This geometry is constrained by the requirement of kappa-symmetry on the boundary together with the use of the equations of motion for the fermions. There are two constraints which are formally similar to those that arise in the abelian case but which differ because of the dependence on the additional coordinates. The model, when quantised, would be a candidate for a fully kappa-symmetric theory of a stack of coincident D-branes including a non-abelian Born-Infeld sector. The example of the D9-brane in a flat background is studied. The constraints on the non-abelian field strength are shown to be in agreement with those derived from the pure spinor approach to the superstring. A covariant formalism is developed and the problem of quantisation is discussed.