arXiv subjects

Ulf Lindstrom

Publications and source records attributed to Ulf Lindstrom.

At least 37 records · Page 2Linked to original sources

arXiv2007

Linearizing Generalized Kahler Geometry

The geometry of the target space of an N=(2,2) supersymmetry sigma-model carries a generalized Kahler structure. There always exists a real function, the generalized Kahler potential K, that encodes all the relevant local differential geometry data: the metric, the B-field, etc. Generically this data is given by nonlinear functions of the second derivatives of K. We show that, at least locally, the nonlinearity on any generalized Kahler manifold can be explained as arising from a quotient of a space without this nonlinearity.

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arXiv2006

Generalized Kahler Geometry from supersymmetric sigma models

We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri regarding the equivalence between generalized Kahler geometry and the bi-hermitean geometry of Gates-Hull-Rocek. When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.

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arXiv2006

SIM(2) and Superspace

In this brief note we give a superspace description of the supersymmetric nonlocal Lorentz noninvariant actions recently proposed by Cohen and Freedman. This leads us to discover similar terms for gauge fields.

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arXiv2006

First-order supersymmetric sigma models and target space geometry

We study the conditions under which N=(1,1) generalized sigma models support an extension to N=(2,2). The enhanced supersymmetry is related to the target space complex geometry. Concentrating on a simple situation, related to Poisson sigma models, we develop a language that may help us analyze more complicated models in the future. In particular, we uncover a geometrical framework which contains generalized complex geometry as a special case.

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arXiv2006

Ricci-flat supertwistor spaces

We show that supertwistor spaces constructed as a Kahler quotient of a hyperkahler cone (HKC) with equal numbers of bosonic and fermionic coordinates are Ricci-flat, and hence, Calabi-Yau. We study deformations of the supertwistor space induced from deformations of the HKC. We also discuss general infinitesimal deformations that preserve Ricci-flatness.

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arXiv2006

Generalized Kahler manifolds and off-shell supersymmetry

We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace description. We construct and explain the geometric significance of the generalized Kahler potential for any generalized Kahler manifold; this potential is the superspace Lagrangian.

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arXiv2005

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

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 Kahler geometry. The metric, B-field and generalized complex structures are all determined in terms of a potential K.

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arXiv2005

T-duality for the sigma model with boundaries

We derive the most general local boundary conditions necessary for T-duality to be compatible with superconformal invariance of the two-dimensional N=1 supersymmetric nonlinear sigma model with boundaries. To this end, we construct a consistent gauge invariant parent action by gauging a U(1) isometry, with and without boundary interactions. We investigate the behaviour of the boundary conditions under T-duality, and interpret the results in terms of D-branes.

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arXiv2004

Generalized complex manifolds and supersymmetry

We find a worldsheet realization of generalized complex geometry, a notion introduced recently by Hitchin which interpolates between complex and symplectic manifolds. The two-dimensional model we construct is a supersymmetric relative of the Poisson sigma model used in context of deformation quantization.

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arXiv2004

Generalized complex geometry and supersymmetric non-linear sigma models

After an elementary presentation of the relation between supersymmetric nonlinear sigma models and geometry, I focus on 2D and the target space geometry allowed when there is an extra supersymmetry. This leads to a brief introduction to generalized complex geometry, a notion introduced recently by Hitchin which interpolates between complex and symplectic manifolds. Finally I present worldsheet realizations of this geometry,

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arXiv2004

Generalized N=(2,2) Supersymmetric Non-Linear Sigma Models

We rewrite the N=(2,2) non-linear sigma model using auxiliary spinorial superfields defining the model on ${\cal T}\oplus^ *{\cal T}$, where ${\cal T}$ is the tangent bundle of the target space. This is motivated by possible connections to Hitchin's generalized complex structures. We find the general form of the second supersymmetry compatible with that of the original model.

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arXiv2004

Type IIB tensionless superstrings in a pp-wave background

We solve the tensionless string in a constant plane wave background and obtain a hugely degenerate spectrum. This is the case for a large class of plane wave backgrounds. We show that the solution can also be derived as a consistent limit of the quantized tensile theory of IIB strings in a pp-wave. This is in contrast to the situation for several other backgrounds.

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arXiv2004

Tensionless Strings, WZW Models at Critical Level and Massless Higher Spin Fields

We discuss the notion of tensionless limit in quantum bosonic string theory, especially in flat Minkowski space, noncompact group manifolds (e.g., SL(2,R)) and coset manifolds (e.g., AdS). We show that in curved space typically there exists a critical value of the tension which is related to the critical value of the level of the corresponding affine algebra. We argue that at the critical level the sring theory becomes tensionless and that there exists a huge new symmetry of the theory. We dicuss the appearence of the higher spin massless states at the critical level.

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arXiv2004

N=1 supersymmetric sigma model with boundaries, II

We consider the N=1 supersymmetric two-dimensional non-linear sigma model with boundaries and nonzero B-field. By analysing the appropriate currents we describe the full set of boundary conditions compatible with N=1 superconformal symmetry. Using this result the problem of finding a correct action is discussed. We interpret the supersymmetric boundary conditions as a maximal integral submanifold of the target space manifold, and speculate about a new geometrical structure, the deformation of an almost product structure.

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arXiv2003

Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields

We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space.

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arXiv2003

Comments on Dualities on Group Manifolds and Supersymmetry

We review some facts about various T-dualities and sigma models on group manifolds, with particular emphasis on supersymmetry. We point out some of the problems in reconciling Poisson-Lie duality with the bi-hermitean geometry of N=2 supersymmetric sigma models. A couple of examples of supersymmetric models admitting Poisson-Lie duality are included.

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arXiv2003

Superconformal boundary conditions for the WZW model

We review the most general, local, superconformal boundary conditions for the two-dimensional N=1 and N=2 non-linear sigma models, and analyse them for the N=1 and N=2 supersymmetric WZW models. We find that the gluing map between the left and right affine currents is generalised in a very specific way as compared to the constant Lie algebra automorphisms that are known.

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arXiv2003

SL(2,Z) tensionless string backgrounds in IIB string theory

We examine a tensionless limit of a SL(2,Z) set of background solutions to IIB supergravity theory, obtained by performing an infinite boost. This yields a solution that corresponds to taking the original string tension to zero. The limit reproduces ordinary Minkowski space except for a delta-like singularity along the string. We study the field content and the energy momentum tensor.

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