Superforms and the CPN−1{\mathbb{C}}{P}^{N-1}CPN−1 supersymmetric sigma model (original) (raw)

Superforms and the CP N−1 supersymmetric sigma model

2015

We present a characterisation of Maurer-Cartan 1-superforms associated to the two-dimensional supersymmetric CP N 1 sigma model. We, then, solve the associated linear spectral problem and use its solutions to describe an integrable system for a su(N)-valued map.

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.

General solutions of the supersymmetric ℂP2 sigma model and its generalisation to ℂPN−1

Journal of Mathematical Physics, 2016

A new approach for the construction of finite action solutions of the supersymmetric CP N−1 sigma model is presented. We show that this approach produces more nonholomorphic solutions than those obtained in previous approaches. We study the CP 2 model in detail and present its solutions in an explicit form. We also show how to generalise this construction to N > 3.

Supersymmetric Sigma Model Geometry

Symmetry, 2012

This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)kähler reduction; projective superspace; the generalized Legendre construction; generalized Kähler geometry and constructions of hyperkähler metrics on Hermitian symmetric spaces.

The sigma model on complex projective superspaces

Journal of High Energy Physics, 2010

The sigma model on projective superspaces CP S−1|S gives rise to a continuous family of interacting 2D conformal field theories which are parametrized by the curvature radius R and the theta angle θ. Our main goal is to determine the spectrum of the model, non-perturbatively as a function of both parameters. We succeed to do so for all open boundary conditions preserving the full global symmetry of the model. In string theory parlor, these correspond to volume filling branes that are equipped with a monopole line bundle and connection. The paper consists of two parts. In the first part, we approach the problem within the continuum formulation. Combining combinatorial arguments with perturbative studies and some simple free field calculations, we determine a closed formula for the partition function of the theory. This is then tested numerically in the second part. There we extend the proposal of [arXiv:0908.1081] for a spin chain regularization of the CP S−1|S model with open boundary conditions and use it to determine the spectrum at the conformal fixed point. The numerical results are in remarkable agreement with the continuum analysis.

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.

N = 1 Supersymmetric Sigma Model with Boundaries, I

Communications in Mathematical Physics, 2003

Supersymmetric σ-models and graded Lie groups

Il Nuovo Cimento A, 1981

A geometrical treatment of supersymmetric a-models of ordinary and graded manifolds in given. The action is written in terms of differential forms on superspace, by means of a modified version of the Berezin duality operation. The linear sets associated to the models are explicitly exhibited and the ((reduction , > problem is discussed. 1.-Introduction. Recently a certain amount of interest has been devoted to supersymmetric generalizations of nonlinear a-models. Important results have been obtained by the study of On and CP~ supersymmetric a-models (1) both at the classical and at the quantum level. Moreover, a general treatment of supersymmetric models on Kghler manifolds (3) has been given and supersymmetrie generalizations of principal chirul (3) and symmetric space (4) a-models have been thoroughly discussed. In all these cases the models are obtained by graduation of the two-dimensional space-time, (*) To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.

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.

Superforms and the CPN−1{\mathbb{C}}{P}^{N-1}CPN−1 supersymmetric sigma model (original) (raw)

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