Supersymmetric Sigma Model Geometry

Lindström, Ulf

doi:10.3390/sym4030474

Cited by 2 publications

(3 citation statements)

References 79 publications

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“…For any supersymmetric nonlinear sigma model, an isometry of its target space, X, forms a global symmetry of the action [19]. Call the isometry group G. An isometry is generated by a set of Killing vector fields, V a , where a = 1, .…”

Section: Isometries Of the Target Space In Sigma Modelsmentioning

confidence: 99%

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Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras

et al. 2018

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We study the ground states and left-excited states of the A k−1 N = (2, 0) little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP 1 with target space the based loop group of SU (k). The ground states, described by L 2 -cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.In loving memory of See-Hong Tan.

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Section: Isometries Of the Target Space In Sigma Modelsmentioning

confidence: 99%

“…(4.5) 19 The Sugawara construction can be used on the affine Lie algebra generators to obtain a grading operator L0, which acts on (4.2) to give the eigenvalue ε − n1 − n2 − n3 . .…”

Section: Module Over Affine Lie Algebramentioning

confidence: 99%

Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras

et al. 2018

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“…Similar to the name of bihypercomplex geometry[16] 5. If we consider J 1 .J 2 = a 1 J 1 + a 2 J 2 + a 3 J 3 then by use of (32) we conclude J 1 .J 2 = ±J 3 6.…”

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confidence: 90%

Algebraic Structures of N=(4,4) and N=(8,8) SUSY Sigma Models on Lie groups and SUSY WZW Models

Aali-Javanangrouh¹,

Rezaei-Aghdam²

2014

Preprint

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Algebraic structures of N = (4, 4) and N = (8, 8) supersymmetric (SUSY) two dimensional sigma models on Lie groups (in general) and SUSY Wess-Zumino-Witten (WZW) models (as special) are obtained. For SUSY WZW models, these algebraic structures are reduced to Lie bialgebraic structures as for the N = (2, 2) SUSY WZW case; with the difference that there is a one 2-cocycle for the N = (4, 4) case and there are two 2-cocycles for the N = (8, 8) case. In general, we show that N = (8, 8) SUSY structure on Lie algebra must be constructed from two N = (4, 4) SUSY structures and in special there must be two 2-cocycles for Manin triples (one 2-cocycle for each of the N = (4, 4) structures). Some examples are investigated. In this way, a calculational method for classifying the N = (4, 4) and N = (8, 8) structures on Lie algebras and Lie groups are obtained.

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Supersymmetric Sigma Model Geometry

Cited by 2 publications

References 79 publications

Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras

Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras

Algebraic Structures of N=(4,4) and N=(8,8) SUSY Sigma Models on Lie groups and SUSY WZW Models

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