Curving Yang-Mills-Higgs gauge theories

Kotov, Alexei; Strobl, Thomas

doi:10.1103/physrevd.92.085032

Cited by 19 publications

(43 citation statements)

References 13 publications

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“…The Lie algebroid gauging procedure outlined by Kotov, Mayer, Strobl and CDJ [22,19,17,13,5] is only valid when (Q| X(Σ) , [·, ·] X(Σ) , ρ X(Σ) )-the restriction of (Q, [·, ·] Q , ρ) to the image of X-is a bundle of Lie algebras.…”

Section: Pullback Constraint Of Kotov-strobl Gaugingmentioning

confidence: 99%

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Lie algebroid gauging of non-linear sigma models

Wright

2019

Journal of Geometry and Physics

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This paper examines a proposal for gauging non-linear sigma models with respect to a Lie algebroid action. The general conditions for gauging a non-linear sigma model with a set of involutive vector fields are given. We show that it is always possible to find a set of vector fields which will (locally) admit a Lie algebroid gauging. Furthermore, the gauging process is not unique; if the vector fields span the tangent space of the manifold, there is a free choice of a flat connection. Ensuring that the gauged action is equivalent to the ungauged action imposes the real constraint of the Lie algebroid gauging proposal. It does not appear possible (in general) to find a field strength term which can be added to the action via a Lagrange multiplier to impose the equivalence of the gauged and ungauged actions. This prevents the proposal from being used to extend T-duality. Integrability of local Lie algebroid actions to global Lie groupoid actions is discussed.

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Section: Pullback Constraint Of Kotov-strobl Gaugingmentioning

confidence: 99%

“…A gauging procedure for non-linear sigma models based on Lie algebroids has appeared in the literature [22,17,13,19]. In principal this proposal gives a vast generalisation to the notion of gauging a non-linear sigma model.…”

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confidence: 99%

Lie algebroid gauging of non-linear sigma models

Wright

2019

Journal of Geometry and Physics

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“…In [15], this setting was extended by precisely such a fiber metric: the main driving motivation for this study was given by an action functional which generalizes the Yang-Mills model with Higgs fields by replacing its structure Lie group together with its action on the space of Higgs fields M by a more general Lie groupoid over M. The functional of this Curved Yang-Mills-Higgs model (CYMH) is defined whenever one is given the following data: a Lorentzian manifold (Σ, γ), which serves as the space-time manifold of the theory, and a Riemannian manifold (M, g) together with a Lie algebroid (A, ρ) over M, which is supplied with a fiber metric κ and a linear connection ∇, as well as an A-valued 2-form B on M. The fields of CYMH are bundle maps from the source tangent bundle T Σ to the target Lie algebroid A viewed as a vector bundle over M. The following theorem provides the compatibility conditions between the data on the target.…”

Section: Introductionmentioning

confidence: 99%

“…Theorem 0.1 (Kotov-Strobl, [15]). The CYMH-functional S CY M H [15] is gauge invariant if and only if the following conditions hold:…”

Section: Introductionmentioning

confidence: 99%

Integration of quadratic Lie algebroids to Riemannian Cartan–Lie groupoids

Kotov

Strobl

2018

Lett Math Phys

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Cartan-Lie algebroids, i.e. Lie algebroids equipped with a compatible connection, permit the definition of an adjoint representation, on the fiber as well as on the tangent of the base. We call (positive) quadratic Lie algebroids, Cartan-Lie algebroids with ad-invariant (Riemannian) metrics on their fibers and base κ and g, respectively. We determine the necessary and sufficient conditions for a positive quadratic Lie algebroid to integrate to a Riemmanian Cartan-Lie groupoid. Here we mean a Cartan-Lie groupoid G equipped with a bi-invariant and inversion invariant metric η on T G such that it induces by submersion the metric g on its base and its restriction to the t-fibers coincides with κ.

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“…[6,13], where T-duality with isometry was studied. 3 The geometric interpretation of ω as a connection 1-form was first introduced in [20] (see also [26]); one can then introduce the corresponding exterior covariant derivative…”

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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Curving Yang-Mills-Higgs gauge theories

Cited by 19 publications

References 13 publications

Lie algebroid gauging of non-linear sigma models

Lie algebroid gauging of non-linear sigma models

Integration of quadratic Lie algebroids to Riemannian Cartan–Lie groupoids

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

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