Dirac sigma models from gauging

Salnikov, Vladimir; Strobl, Thomas

doi:10.1007/jhep11(2013)110

Cited by 17 publications

(20 citation statements)

References 36 publications

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“…This section is mainly a review following the ideas of [41]; the lifting to the tangent, that will be important in the end for our application, is inspired by its sequels [28,42].…”

Section: Basics Of the Q -Formalismmentioning

confidence: 99%

Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions

Lavau

Samtleben

Strobl

2014

Journal of Geometry and Physics

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a b s t r a c tWe disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six space-time dimensions. This is a coupled system of 1-form, 2-form, and 3-form gauge fields. We show that the algebraic consistency constraints governing this system permit to define a Lie 3-algebra, generalizing the structural Lie algebra of a standard Yang-Mills theory to the setting of a higher bundle. Reformulating the Lie 3-algebra in terms of a nilpotent degree 1 BRST-type operator Q , this higher bundle can be compactly described by means of a Q -bundle; its fiber is the shifted tangent of the Q -manifold corresponding to the Lie 3-algebra and its base the odd tangent bundle of space-time equipped with the de Rham differential. The generalized Bianchi identities can then be retrieved concisely from Q 2 = 0, which encode all the essence of the structural identities. Gauge transformations are identified as vertical inner automorphisms of such a bundle, their algebra being determined from a Q -derived bracket.

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“…This section is mainly a review following the ideas of [41]; the lifting to the tangent, that will be important in the end for our application, is inspired by its sequels [28,42].…”

Section: Basics Of the Q -Formalismmentioning

confidence: 99%

Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions

Lavau

Samtleben

Strobl

2014

Journal of Geometry and Physics

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“…This is the central result of this paper. Additionally, it will allow us to find the form of the gauge symmetries for Dirac σ-models, which are very general two-dimensional topological field theories interpolating between WZW models and Poisson σ-models and they were introduced in [23,24]. Our analysis will be complemented with an explicit example where we will apply our findings to the WZ Poisson σ-model with a kinetic term.…”

Section: Introductionmentioning

confidence: 94%

“…At the availability of a metric g on M, which is the case here, yet another parametrization of Dirac structures is possible, as explained in [23,24]. Instead of referring to the generalized vectors ξ a = ρ a + θ a , one uses the Riemannian metric g to identify T M with T * M and introduces an orthogonal operator O = O i j ∂ i ⊗ dX j ∈ Γ(End(T M)) whose graph is the Dirac structure D. The role of this operator is that for any element, say v ⊕ η with v a vector and η an 1-form, of the Dirac structure there exists a unique section a of T M such…”

Section: Dirac Structures and Dirac σ-Modelsmentioning

confidence: 99%

Beyond the standard gauging: gauge symmetries of Dirac sigma models

Chatzistavrakidis

Deser

Jonke

et al. 2016

J. High Energ. Phys.

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In this paper we study the general conditions that have to be met for a gauged extension of a two-dimensional bosonic σ-model to exist. In an inversion of the usual approach of identifying a global symmetry and then promoting it to a local one, we focus directly on the gauge symmetries of the theory. This allows for action functionals which are gauge invariant for rather general background fields in the sense that their invariance conditions are milder than the usual case. In particular, the vector fields that control the gauging need not be Killing. The relaxation of isometry for the background fields is controlled by two connections on a Lie algebroid L in which the gauge fields take values, in a generalization of the common Lie-algebraic picture. Here we show that these connections can always be determined when L is a Dirac structure in the H-twisted Courant algebroid. This also leads us to a derivation of the general form for the gauge symmetries of a wide class of two-dimensional topological field theories called Dirac σ-models, which interpolate between the G/G Wess-Zumino-Witten model and the (Wess-Zumino-term twisted) Poisson sigma model.

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“…[16][17][18][19][20]. The essence of this formulation relies on an extension of the standard infinitesimal gauge transformations for the gauge fields A a to include a part proportional to DX i , where X i are the world sheet scalars and DX i is the gauge covariant derivative on the world sheet obtained by minimal coupling.…”

Section: Jhep01(2016)154mentioning

confidence: 99%

“…In order to proceed, we have to use some properties of step 2 nilmanifolds. To this end we consider the splitting of the indices a = (a 0 ,ā) such that C identically, and 18) provided that…”

Section: A Class Of Examplesmentioning

confidence: 99%

T-duality without isometry via extended gauge symmetries of 2D sigma models

Chatzistavrakidis

Deser

Jonke

2016

J. High Energ. Phys.

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Target space duality is one of the most profound properties of string theory. However it customarily requires that the background fields satisfy certain invariance conditions in order to perform it consistently; for instance the vector fields along the directions that T-duality is performed have to generate isometries. In the present paper we examine in detail the possibility to perform T-duality along non-isometric directions. In particular, based on a recent work of Kotov and Strobl, we study gauged 2D sigma models where gauge invariance for an extended set of gauge transformations imposes weaker constraints than in the standard case, notably the corresponding vector fields are not Killing. This formulation enables us to follow a procedure analogous to the derivation of the Buscher rules and obtain two dual models, by integrating out once the Lagrange multipliers and once the gauge fields. We show that this construction indeed works in non-trivial cases by examining an explicit class of examples based on step 2 nilmanifolds.

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Dirac sigma models from gauging

Cited by 17 publications

References 36 publications

Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions

Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions

Beyond the standard gauging: gauge symmetries of Dirac sigma models

T-duality without isometry via extended gauge symmetries of 2D sigma models

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