Double field theory algebroid and curved <i>L</i>
                  <i>∞</i>-algebras

Grewcoe, Clay James; Jonke, Larisa

doi:10.1063/5.0041479

Cited by 13 publications

(9 citation statements)

References 51 publications

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“…Besides the BV action, it would be interesting to investigate the relation of the (bi-)twisted R-Poisson topological field theories to constructions in terms of L ∞ algebras, for example within the higher gauge theory approach of [42]. Interestingly, a direct construction of membrane sigma models in terms of L ∞ algebras was recently discussed in [43] and also extended to curved L ∞ algebras [44]. From a different point of view, it would also be desirable to understand twisted R-Poisson structures in the context of P ∞ (homotopy Poisson) structures described in [45] (see also [46] for recent applications of this idea).…”

Section: Jhep09(2021)045mentioning

confidence: 99%

Topological field theories induced by twisted R-Poisson structure in any dimension

Chatzistavrakidis

2021

J. High Energ. Phys.

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We construct a class of topological field theories with Wess-Zumino term in spacetime dimensions ≥ 2 whose target space has a geometrical structure that suitably generalizes Poisson or twisted Poisson manifolds. Assuming a field content comprising a set of scalar fields accompanied by gauge fields of degree (1, p − 1, p) we determine a generic Wess-Zumino topological field theory in p + 1 dimensions with background data consisting of a Poisson 2-vector, a (p + 1)-vector R and a (p + 2)-form H satisfying a specific geometrical condition that defines a H-twisted R-Poisson structure of order p + 1. For this class of theories we demonstrate how a target space covariant formulation can be found by means of an auxiliary connection without torsion. Furthermore, we study admissible deformations of the generic class in special spacetime dimensions and find that they exist in dimensions 2, 3 and 4. The two-dimensional deformed field theory includes the twisted Poisson sigma model, whereas in three dimensions we find a more general structure that we call bi-twisted R-Poisson. This extends the twisted R-Poisson structure of order 3 by a non-closed 3-form and gives rise to a topological field theory whose covariant formulation requires a connection with torsion and includes a twisted Poisson sigma model in three dimensions as a special case. The relation of the corresponding structures to differential graded Q-manifolds based on the degree shifted cotangent bundle T*[p]T*[1]M is discussed, as well as the obstruction to them being QP-manifolds due to the Wess-Zumino term.

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Section: Jhep09(2021)045mentioning

confidence: 99%

Topological field theories induced by twisted R-Poisson structure in any dimension

Chatzistavrakidis

2021

J. High Energ. Phys.

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Section: Discussionmentioning

confidence: 99%

Topological Field Theories induced by twisted R-Poisson structure in any dimension

Chatzistavrakidis

2021

Preprint

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We construct a class of topological field theories with Wess-Zumino term in spacetime dimensions ≥ 2 whose target space has a geometrical structure that suitably generalizes Poisson or twisted Poisson manifolds. Assuming a field content comprising a set of scalar fields accompanied by gauge fields of degree (1, p − 1, p) we determine a generic Wess-Zumino topological field theory in p + 1 dimensions with background data consisting of a Poisson 2-vector, a (p + 1)-vector R and a (p + 2)-form H satisfying a specific geometrical condition that defines a H-twisted R-Poisson structure of order p + 1. For this class of theories we demonstrate how a target space covariant formulation can be found by means of an auxiliary connection without torsion. Furthermore, we study admissible deformations of the generic class in special spacetime dimensions and find that they exist in dimensions 2, 3 and 4. The two-dimensional deformed field theory includes the twisted Poisson sigma model, whereas in three dimensions we find a more general structure that we call bi-twisted R-Poisson. This extends the twisted R-Poisson structure of order 3 by a non-closed 3-form and gives rise to a topological field theory whose covariant formulation requires a connection with torsion and includes a twisted Poisson sigma model in three dimensions as a special case. The relation of the corresponding structures to differential graded Qmanifolds based on the degree shifted cotangent bundle T * [p]T * [1]M is discussed, as well as the obstruction to them being QP-manifolds due to the Wess-Zumino term.

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“…Moreover, an interesting connection has been established between the L ∞ bootstrap and symplectic embeddings of non-commutative algebras [6,7]. It is worth mentioning that the role of L ∞ algebras in gauge and field theory is already investigated in [8][9][10], see also [11][12][13][14][15][16] for recent progresses in studies of the L ∞ structures in the field theoretic context.…”

Section: Introductionmentioning

confidence: 99%

Four-dimensional noncommutative deformations of U(1) gauge theory and L∞ bootstrap.

Kurkov

Vitale

2022

J. High Energ. Phys.

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We construct a family of four-dimensional noncommutative deformations of U(1) gauge theory following a general scheme, recently proposed in JHEP 08 (2020) 041 for a class of coordinate-dependent noncommutative algebras. This class includes the $$ \mathfrak{su} $$ su (2), the $$ \mathfrak{su} $$ su (1, 1) and the angular (or λ-Minkowski) noncommutative structures. We find that the presence of a fourth, commutative coordinate x0 leads to substantial novelties in the expression for the deformed field strength with respect to the corresponding three-dimensional case. The constructed field theoretical models are Poisson gauge theories, which correspond to the semi-classical limit of fully noncommutative gauge theories. Our expressions for the deformed gauge transformations, the deformed field strength and the deformed classical action exhibit flat commutative limits and they are exact in the sense that all orders in the deformation parameter are present. We review the connection of the formalism with the L∞ bootstrap and with symplectic embeddings, and derive the L∞-algebra, which underlies our model.

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Double field theory algebroid and curved L ∞-algebras

Cited by 13 publications

References 51 publications

Topological field theories induced by twisted R-Poisson structure in any dimension

Topological field theories induced by twisted R-Poisson structure in any dimension

Topological Field Theories induced by twisted R-Poisson structure in any dimension

Four-dimensional noncommutative deformations of U(1) gauge theory and L∞ bootstrap.

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