Strings in Singular Space-Times and Their Universal Gauge Theory

Chatzistavrakidis, Athanasios; Deser, Andreas; Jonke, Larisa; Strobl, Thomas

doi:10.1007/s00023-017-0580-3

Cited by 20 publications

(66 citation statements)

References 38 publications

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“…[2], an equally nice reformulation of them such (3.13) for g and B is still missing as of the moment.…”

Section: Pos(corfu2016)087mentioning

confidence: 99%

“…In addition, there is an anchor map ρ : E → T M such that (2.5) holds true (for any s 1 ∈ Γ(E) and s 2 ∈ Γ(E ⊕ F)) and all the other brackets are C ∞ (M)-linear. Likewise for Lie n-algebroids for higher n. 2 Why are Lie algebroids and their higher n generalisations of importance for us in the context of gauging? The reason is that any Lie n-algebroid generates a singular foliation on its base M. Suppose that M is the target space of some scalar fields.…”

Section: Going Beyond Lie Algebras and Standard Geometrymentioning

confidence: 99%

“…In the present paper we will consider foliations coming from an almost Lie algebroid, be it the lower part of some Lie n-algebroid or not. (Some further details on these assumptions and additional information, if one has a Lie or Lie 2-algebroid, can be found in [2]. )…”

Section: Going Beyond Lie Algebras and Standard Geometrymentioning

confidence: 99%

“…A natural line element on this manifold is given as ds 2 Now we would like to gauge this model along some vector fields. For simplicity, here we follow mainly the more standard extension approach along the lines of section 3.…”

mentioning

confidence: 99%

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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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“…[2], an equally nice reformulation of them such (3.13) for g and B is still missing as of the moment.…”

Section: Pos(corfu2016)087mentioning

confidence: 99%

Section: Going Beyond Lie Algebras and Standard Geometrymentioning

confidence: 99%

Section: Going Beyond Lie Algebras and Standard Geometrymentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

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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“…Originating from Buscher's observation this was motivated and extensively used in supergravity . Studying dualities from the sigma‐model point of view uses total spaces of Courant algebroids as target spaces . The mathematical study of T‐duality for principal torus bundles with H ‐flux in the geometric case and beyond showed the need for continuous fields of noncommutative and nonassociative tori .…”

Section: Introductionmentioning

confidence: 99%

Pre‐NQ Manifolds and Correspondence Spaces: the Nilmanifold Example

Deser

2019

Fortschritte der Physik

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Courant algebroids correspond to degree‐2 symplectic differential graded manifolds or NQ‐manifolds for short. We review how a similar construction shows that locally the gauge structure of Double Field Theory corresponds to degree‐2 symplectic pre‐NQ manifolds. To illustrate first steps towards a global understanding of the pre‐NQ case, we apply the local constructions to 3‐dimensional nilmanifolds carrying an abelian gerbe. These are among prime examples where T‐duality is well‐understood and allow us to investigate classic results in the graded language.

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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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Strings in Singular Space-Times and Their Universal Gauge Theory

Cited by 20 publications

References 38 publications

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

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

Pre‐NQ Manifolds and Correspondence Spaces: the Nilmanifold Example

Beyond the standard gauging: gauge symmetries of Dirac sigma models

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