Supersymmetric non-abelian Born-Infeld revisited

We determine the non-abelian Born-Infeld action, including fermions, as it results from the four-point tree-level open superstring scattering amplitudes at order alpha'^2. We find that, after an appropriate field redefinition all terms at this order can be written as a symmetrised trace. We confront this action with the results that follow from kappa-symmetry and conclude that the recently proposed non-abelian kappa-symmetry cannot be extended to cubic orders in the Born-Infeld curvature.Comment: 26 pages, Late

Superspace WZW Models and Black Holes

We show how to write an off-shell action for the $SU(2)\times U(1)$ supersymmetric WZW model in terms of $N=2$ chiral and twisted chiral multiplets. We discuss the $N=4$ supersymmetry of this model and exhibit the $N=4$ superconformal current algebra. Finally, we show that the off-shell formulation makes it possible to perform a duality transformation, which leads to a supersymmetric sigma model on a manifold with a black hole type singularity.Comment: 12 page

Gauged W Algebras

We perform an Hamiltonian reduction on a classical \cw(\cg, \ch) algebra, and prove that we get another \cw(\cg, \ch$'$) algebra, with $\ch\subset\ch'$. In the case \cg=S\ell(n), the existence of a suitable gauge, called Generalized Horizontal Gauge, allows to relate in this way two \cw-algebras as soon as their corresponding \ch-algebras are related by inclusion.Comment: 11 p., Latex. There was a misprint on the last autho

A derivation of the BRST operator for non-critical W-strings:Dedicated to Professor F. Cerulus on the occasion of his 65th Birthday

We derive the recently proposed BRST charge for non-critical W strings from a lagrangian approach. The basic observation is that, despite appearances, the combination of two classical "matter" and "Toda" w3 systems leads to a closed modified gauge algebra, which is of the so-called soft type. Based on these observations, a novel way to construct critical w3 strings is given.</p

Strings from N=2N=2 Gauged Wess-Zumino-Witten Models

We present an algebraic approach to string theory. An embedding of $sl(2|1)$ in a super Lie algebra together with a grading on the Lie algebra determines a nilpotent subalgebra of the super Lie algebra. Chirally gauging this subalgebra in the corresponding Wess-Zumino-Witten model, breaks the affine symmetry of the Wess-Zumino-Witten model to some extension of the $N=2$ superconformal algebra. The extension is completely determined by the $sl(2|1)$ embedding. The realization of the superconformal algebra is determined by the grading. For a particular choice of grading, one obtains in this way, after twisting, the BRST structure of a string theory. We classify all embeddings of $sl(2|1)$ into Lie super algebras and give a detailed account of the branching of the adjoint representation. This provides an exhaustive classification and characterization of both all extended $N=2$ superconformal algebras and all string theories which can be obtained in this way.Comment: 50 pages, LaTe

On the Lagrangian Realization of Non-Critical W{\cal W}-Strings

A large class of non-critical string theories with extended worldsheet gauge symmetry are described by two coupled, gauged Wess-Zumino-Witten Models. We give a detailed analysis of the gauge invariant action and in particular the gauge fixing procedure and the resulting BRST symmetries. The results are applied to the example of ${\cal W}_3$ strings.Comment: 19 pages, LaTeX (REVTEX macro's

The BRST Operator for the Large N=4N=4 Superconformal Algebra

We review the detailed structure of the large $N=4$ superconformal algebra, and construct its BRST operator which constitutes the main object for analyzing $N=4$ strings. We then derive the general condition for the nilpotency of the BRST operator and show that there exists a line of critical $N=4$ string theories.Comment: Latex file, 16 pages, NBI-HE-94-1

Towards a supersymmetric non-abelian Born-Infeld theory

We define an iterative procedure to obtain a non-abelian generalization of the Born-Infeld action. This construction is made possible by the use of the severe restrictions imposed by kappa-symmetry. We have calculated all bosonic terms in the action up to terms quartic in the Yang-Mills field strength and all fermion bilinear terms up to terms cubic in the field strength. Already at this order the fermionic terms do not satisfy the symmetric trace-prescription.Comment: 9 pp. Latex, to appear in the proceedings of the Strings 2000 conferenc

Supersymmetric non-linear sigma-models with boundaries revisited

We study two-dimensional supersymmetric non-linear sigma-models with boundaries. We derive the most general family of boundary conditions in the non-supersymmetric case. Next we show that no further conditions arise when passing to the N=1 model. We present a manifest N=1 off-shell formulation. The analysis is greatly simplified compared to previous studies and there is no need to introduce non-local superspaces nor to go (partially) on-shell. Whether or not torsion is present does not modify the discussion. Subsequently, we determine under which conditions a second supersymmetry exists. As for the case without boundaries, two covariantly constant complex structures are needed. However, because of the presence of the boundary, one gets expressed in terms of the other one and the remainder of the geometric data. Finally we recast some of our results in N=2 superspace and discuss applications.Comment: LaTeX, 23 page

Diverse N=(4,4){\cal N} =(4,4) Twisted Multiplets in N=(2,2){\cal N} = (2,2) Superspace

We describe four different types of the ${\cal N} = (4,4)$ twisted supermultiplets in two-dimensional ${\cal N} = (2,2)$ superspace ${\bf R}^{1,1|2,2}$. All these multiplets are presented by a pair of chiral and twisted chiral superfields and differ in the transformation properties under an extra hidden ${\cal N} = (2,2)$ supersymmetry. The sigma model ${\cal N} = (2,2)$ superfield Lagrangians for each type of the ${\cal N} = (4,4)$ twisted supermultiplets are real functions subjected to some differential constraints implied by the hidden supersymmetry. We prove that the general sigma model action, with all types of ${\cal N} = (4,4)$ twisted multiplets originally included, is reduced to a sum of sigma model actions for separate types. An interaction between the multiplets of different sorts is possible only through the appropriate mass terms, and only for those multiplets which belong to the same `self-dual' pair.Comment: 21 p., Late