2d gauge theories and generalized geometry

Kotov, Alexei; Salnikov, Vladimir; Strobl, Thomas

doi:10.1007/jhep08(2014)021

Cited by 16 publications

(30 citation statements)

References 26 publications

(59 reference statements)

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“…Such systems have been under investigation for their relation to the yet elusive dynamics of multiple M5 branes, see e.g., [20][21][22][23][24][25][26]. A similar analysis of the general tensor hierarchy developed in [7] will be presented in a forthcoming paper [27].…”

Section: Introductionmentioning

confidence: 97%

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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Section: Introductionmentioning

confidence: 97%

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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“…Thus it is natural to wonder whether one can construct gauge field theories without having at hand a group action, working directly at the level of foliations. Such a task was undertaken in our recent work [1,2], building on [3][4][5]. In this contribution we review and clarify the main ideas and some of the results found there, namely on the gauging of a singular foliation in the case of 2D bosonic σ -models.…”

Section: Introduction and Motivationsmentioning

confidence: 90%

“…Such an action was first studied in [35] and more recently in [5,37,38]. As in the minimally coupled case, we examine the gauge invariance of S W Z under the transformations δ ε X i and δ ε A a .…”

Section: On the Construction Of Gauge Theories: The Traditional And Tmentioning

confidence: 99%

Gauging as constraining: the universal generalised geometry action in two dimensions

Chatzistavrakidis¹,

Deser²,

Jonke³

et al. 2017

Proceedings of Corfu Summer Institute 2016 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2016)

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One of the central concepts in modern theoretical physics, gauge symmetry, is typically realised by lifting a finite-dimensional global symmetry group of a given functional to an infinite-dimensional local one by extending the functional to include gauge fields. In this contribution we review the construction of gauged actions for two-dimensional sigma models, considering a more general notion to be gauged, namely that of a (possibly singular) foliation. In particular, the original action does not need to have any global symmetry for this purpose. Moreover, reformulating the ungauged theory by means of auxiliary 1-form fields taking values in the generalised tangent bundle over the target, all possible such gauge theories result from restriction of these fields to take values in (possibly small) Dirac structures. This turns all the remaining 1-form fields into gauge fields and leads to the presence of a local symmetry. We recall all needed mathematical notions, those of (higher) Lie algebroids, Courant algebroids, and Dirac structures.

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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%

“…Recall that the 2-form that multiplies the Lagrange multipliers in Buscher's procedure is precisely the field strength of the corresponding gauge fields. In the present formulation this turns out to be 19) which is the same as the one considered in ref. [20].…”

Section: Jhep01(2016)154mentioning

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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2d gauge theories and generalized geometry

Cited by 16 publications

References 26 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

Gauging as constraining: the universal generalised geometry action in two dimensions

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

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