Alexander Sevrin

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 02 . Wend that,after anappropriateeld redenition allterms at this order canbewrittenasasymmetrised trace. Weconfront thisactionwiththeresultsthat 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.

The M-theory two-brane in AdS4×S7 and AdS7×S4

Abstract We construct the supermembrane action in an AdS4×S7 and AdS7×S4 background to all orders in anticommuting coordinates. The result is compared to and agrees completely with results obtained earlier for generic supergravity backgrounds through gauge completion at low orders in θ.

NON-ABELIAN BORN-INFELD VERSUS STRING THEORY

Motivated by the results of Hashimoto and Taylor, we perform a detailed study of the mass spectrum of the non-abelian Born-Infeld theory, defined by the symmetrized trace prescription, on tori with constant magnetic fields turned on. Subsequently, we compare this for several cases to the mass spectrum of intersecting D-branes. Exact agreement is found in only two cases: BPS configurations on the four-torus and coinciding tilted branes. Finally we investigate the fluctuation dynamics of an arbitrarily wrapped Dp-brane with flux.

Off-shell formulation of N = 2 non-linear σ-models

Abstract We study d = 2, N = (2, 2) non-linear σ-models in (2, 2) superspace. By analyzing the most general constraints on a superfield, we show that through an appropriate choice of coordinates, there are no other superfields than chiral, twisted chiral and semi-chiral ones. We study the resulting σ-models and we speculate on the possibility that all (2, 2) non-linear σ-models can be described using these fields. We apply the results to two examples: the SU (2) × U(1) and the SU (2) × SU (2) WZW model. Pending upon the choice of complex structures, and former can be described in terms of either one semi-chiral multiplet or a chiral and a twisted chiral multiplet. The latter is formulated in terms of one semi-chiral and one twisted chiral multiplet. For both cases we obtain the potential explicitly.

The non-abelian Born–Infeld action at order F6

Abstract To gain insight into the non-abelian Born–Infeld (NBI) action, we study coinciding D-branes wrapped on tori, and turn on magnetic fields on their worldvolume. We then compare predictions for the spectrum of open strings stretching between these D-branes, from perturbative string theory and from the effective NBI action. Under some plausible assumptions, we find corrections to the Str-prescription for the NBI action at order F 6 . In the process we give a way to classify terms in the NBI action that can be written in terms of field strengths only, in terms of permutation group theory.

Properties of semi-chiral superfields

Whenever the N=(2,2) supersymmetry algebra of non-linear σ-models in two dimensions does not close off-shell, a holomorphic two-form can be defined. The only known superfields providing candidate auxiliary fields to achieve an off-shell formulation are semi-chiral fields. Such a semi-chiral description is only possible when the two-form is constant. Using an explicit example, hyper-Kahler manifolds, we show that this is not always the case. Finally, we give a concrete construction of semi-chiral potentials for a class of hyper-Kahler manifolds using the duality exchanging a pair consisting of a chiral and a twisted-chiral superfield for one semi-chiral multiplet.

Chiral Forms and Their Deformations

Abstract: We systematically study deformations of chiral forms with applications to string theory in mind. To first order in the coupling constant, this problem can be translated into the calculation of the local BRST cohomological group at ghost number zero. We completely solve this cohomology and present detailed proofs of results announced in a previous letter. In particular, we show that there is no room for non-abelian, local, deformations of a pure system of chiral p-forms.

Deformations of chiral two forms in six-dimensions

Abstract Motivated by a system consisting of a number of parallel M5-branes, we study possible local deformations of chiral two-forms in six dimensions. Working to first order in the coupling constant, this reduces to the study of the local BRST cohomological group at ghost number zero. We obtain an exhaustive list of all possible deformations. None of them allows for a satisfactory formulation of the M5-branes system leading to the conclusion that no local field theory can describe such a system.

Some aspects of N = (2, 2), D = 2 supersymmetry

The off-shell description of (2, 2) supersymmetric non-linear σ-models is reviewed. The conditions for ultra-violet finiteness are derived and T-duality is discussed in detail.

The quantum geometry of N = (2,2) non-linear σ-models

Abstract We consider a general N = (2,2) non-linear σ-model in (2,2) superspace. Depending on the details of the complex structures involved, an off-shell description can be given in terms of chiral, twisted chiral and semi-chiral superfields. Using superspace techniques, we derive the conditions the potential has to satisfy in order to be ultra-violet finite at one loop. We pay particular attention to the effects due to the presence of semi-chiral superfields. A complet description of N = (2,2) strings follows from this.