Special holonomy sigma models with boundaries (original) (raw)

Special Holonomy and Two-Dimensional Supersymmetric Sigma-Models

Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy are characterized by symmetries related to covariantly constant forms that these manifolds hold, which are generally non-linear and close in a field dependent sense. The thesis explores various aspects of the special holonomy symmetries.

The geometry of supersymmetric sigma-models

We review non-linear σ-models with (2,1) and (2,2) supersymmetry. We focus on off-shell closure of the supersymmetry algebra and give a complete list of (2, 2) superfields. We provide evidence to support the conjecture that all N = (2, 2) non-linear σ-models can be described by these fields. This in its turn leads to interesting consequences about the geometry of the target manifolds. One immediate corollary of this conjecture is the existence of a potential for hyper-Kähler manifolds, different from the Kähler potential, which does not only allow for the computation of the metric, but of the three fundamental twoforms as well. Several examples are provided: WZW models on SU (2) × U (1) and SU (2) × SU (2) and four-dimensional special hyper-Kähler manifolds.

Generalized complex geometry, generalized branes and the Hitchin sigma model

Journal of High Energy Physics, 2005

Hitchin's generalized complex geometry has been shown to be relevant in compactifications of superstring theory with fluxes and is expected to lead to a deeper understanding of mirror symmetry. Gualtieri's notion of generalized complex submanifold seems to be a natural candidate for the description of branes in this context. Recently, we introduced a Batalin-Vilkovisky field theoretic realization of generalized complex geometry, the Hitchin sigma model, extending the well known Poisson sigma model. In this paper, exploiting Gualtieri's formalism, we incorporate branes into the model. A detailed study of the boundary conditions obeyed by the world sheet fields is provided. Finally, it is found that, when branes are present, the classical Batalin-Vilkovisky cohomology contains an extra sector that is related non trivially to a novel cohomology associated with the branes as generalized complex submanifolds.

N = 1 supersymmetric sigma model with boundaries, II

Nuclear Physics B, 2004

We study an N = 1 two-dimensional non-linear sigma model with boundaries representing, e.g., a gauge fixed open string. We describe the full set of boundary conditions compatible with N = 1 superconformal symmetry. The problem is analyzed in two different ways: by studying requirements for invariance of the action, and by studying the conserved supercurrent. We present the target space interpretation of these results, and identify the appearance of partially integrable almost product structures.

Generalized Kahler geometry and manifest N=(2,2) supersymmetric nonlinear sigma-models

Journal of High Energy Physics

Generalized complex geometry is a new mathematical framework that is useful for describing the target space of N = (2, 2) nonlinear sigma-models. The most direct relation is obtained at the N = (1, 1) level when the sigma model is formulated with an additional auxiliary spinorial field. We revive a formulation in terms of N = (2, 2) semi-(anti)chiral multiplets where such auxiliary fields are naturally present. The underlying generalized complex structures are shown to commute (unlike the corresponding ordinary complex structures) and describe a Generalized Kähler geometry. The metric, B-field and generalized complex structures are all determined in terms of a potential K.

Generating branes via sigma models

Physical Review D, 1998

Starting with the D-dimensional Einstein-dilaton-antisymmetric form equations and assuming a block-diagonal form of a metric we derive a (D − d)dimensional σ-model with the target space SL(d, R)/SO(d)×SL(2, R)/SO(2)× R or its non-compact form. Various solution-generating techniques are developed and applied to construct some known and some new p-brane solutions. It is shown that the Harrison transformation belonging to the SL(2, R) subgroup generates black p-branes from the seed Schwarzschild solution. A fluxbrane generalizing the Bonnor-Melvin-Gibbons-Maeda solution is constructed as well as a non-linear superposition of the fluxbrane and a spherical black hole. A new simple way to endow branes with additional internal structure such as plane waves is suggested. Applying the harmonic maps technique we generate new solutions with a non-trivial shell structure in the transverse space ('matrioshka' p-branes). Similar σ-model is constructed for the intersecting branes. It is shown that the intersection rules have a simple geometric interpretation as conditions ensuring the symmetric space property of the target space. The null-geodesic method is used to find intersecting 'matrioshka' pbranes in Type IIA supergravity. Finally, a Bonnor-type symmetry relating the four-dimensional vacuum SL(2, R) with the corresponding sector of the above global symmetry group is used to construct a new magnetic 6-brane with a dipole moment in the ten-dimensional IIA theory.

Generalized Kähler geometry and manifest Script N = (2,2) supersymmetric nonlinear sigma-models

Journal of High Energy Physics, 2005

Generalized complex geometry is a new mathematical framework that is useful for describing the target space of N = (2, 2) nonlinear sigma-models. The most direct relation is obtained at the N = (1, 1) level when the sigma model is formulated with an additional auxiliary spinorial field. We revive a formulation in terms of N = (2, 2) semi-(anti)chiral multiplets where such auxiliary fields are naturally present. The underlying generalized complex structures are shown to commute (unlike the corresponding ordinary complex structures) and describe a Generalized Kähler geometry. The metric, B-field and generalized complex structures are all determined in terms of a potential K.