Superstrings with boundary fermions

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 M , with fermionic fibres, over the super worldvolume M of a D-brane together with a map from M into the N = 2, D = 10 target superspace M . 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.

Multiple M0-brane system in an arbitrary eleven-dimensional supergravity background

“…2 As far as an effective description of multiple brane systems is concerned, it was quickly appreciated that at very low energy the system of N nearly coincident Dp-branes (multiple Dp-brane or mDp system) is described by the maximally supersymmetric d ¼ ðp þ 1Þ-dimensional UðNÞ Yang-Mills model (SYM model) [20]. However, in the problem of constructing a complete (more complete) nonlinear supersymmetric action for multiple Dp-branes, posed in ninetieth [21], only a particular progress could be witnessed (see [22][23][24] for lower-dimensional and lower-codimensional branes as well as [25][26][27] discussed below).…”

Supersymmetric Sigma Model Geometry

“…We have temporarily included a boundary term, which is sometimes needed for open models to have all the symmetries of the bulk-theory [43][44][45], or when there are fields living only on the boundary coupling to the bulk fields as is the well known case for (stacks of) D-branes. For a discussion of the latter in a sigma model context, see [46]. Expanding the superfield as Φ(ξ, θ) = X + θΨ + ..., where X(ξ) and Ψ(ξ) are bosonic and fermionic fields over the even part of Σ (coordinatized by ξ), the action Equation (2) becomes…”

Boundary fermions and the plane wave

“…Before discussing the N = (2, 2) worldsheet supersymmetry, we briefly establish the existence of the spinor η with the requirements (10). Using the properties of the complex Dirac matrices Γ i , Γ ı , the spinor η is immediately determined to…”

“…Going back to [8], the boundary fermions are in this case interpreted as representing Chan-Paton factors. A discussion along these lines in the context of pure spinors is presented in [9] and a treatment using the Green-Schwarz formulation is to be found [10].…”