Higher Dimensional Lie Algebroid Sigma Model with WZ Term

Ikeda, Noriaki

doi:10.3390/universe7100391

Cited by 7 publications

(7 citation statements)

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“…This refers to cases where higher brackets appear and their compatibility with a suitable higher connection is studied. From a field-theoretical perspective such higher analogs of the basic curvature have appeared in local coordinate form in the context of twisted R-Poisson sigma models [33,34] and they were presented in [75]. From a geometric perspective, they were studied in [32].…”

Section: Discussionmentioning

confidence: 99%

“…with respect to the scalar gauge parameter ǫ µ = ǫ µ (σ m ). Having only a scalar gauge parameter is a feature that simplifies matters, as opposed to higher dimensional analogs of the model which have a richer structure but also the additional complication of higher form parameters that lead to reducible gauge symmetries [33,34]. The classical field equations of the theory are…”

Section: Poisson Sigma Model and Basic Curvaturementioning

confidence: 99%

“…It was brought to our attention that this definition was also given recently in[32] in the context of representations up to homotopy for Lie n-algebroids, along with higher analogs thereof. Indications that such higher analogs of a basic curvature tensor appear in higher-dimensional sigma models such as twisted R-Poisson ones are found in[33,34]. These are related to QPn structures including n > 2, but also go beyond them via Wess-Zumino extensions.…”

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confidence: 94%

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Basic curvature and the Atiyah cocycle in gauge theory

Chatzistavrakidis¹,

Jonke²

2023

Preprint

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We study connections on higher structures such as Lie and Courant algebroids and their description as differential graded manifolds and explore the role of their basic curvature tensor and of the Atiyah cocycle in topological sigma models and higher gauge theories. The basic curvature of a connection on a Lie algebroid is a measure for the compatibility of the connection with the Lie bracket and it appears in the BV operator of topological sigma models in 2D. Here we define a basic curvature tensor for connections on Courant algebroids and we show that in the description of a Courant algebroid as a QP manifold it appears naturally as part of the homological vector field together with the Gualtieri torsion of a generalised connection. The Atiyah cocycle of a connection on a differential graded manifold is a measure of the compatibility of the connection with the homological vector field. We argue that in the graded-geometric description of higher gauge theories, the structure of gauge transformations is governed by a Kapranov L ∞ [1] algebra, whose binary bracket is given by the Atiyah cocycle. We also revisit some aspects of derived structures and we uncover the role of the Atiyah cocycle in deriving E-tensors for E-connections on Lie and Courant algebroids from ordinary tensors on differential graded manifolds.

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Section: Discussionmentioning

confidence: 99%

Section: Poisson Sigma Model and Basic Curvaturementioning

confidence: 99%

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confidence: 94%

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Basic curvature and the Atiyah cocycle in gauge theory

Chatzistavrakidis¹,

Jonke²

2023

Preprint

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“…Also one observes that the AKSZ formalism does not produce Wess-Zumino terms, as they are present, e.g. in the H-twisted Poisson sigma model [13] and higher dimensional generalizations thereof [24][25][26], but precisely also in the Dirac sigma model. 9 Either of the two equivalent equations with ± can be used, or alternatively one could sum the two and obtain a more democratic expression.…”

Section: The 'Q Versus Qp Problem'mentioning

confidence: 99%

Topological Dirac sigma models and the classical master equation

Chatzistavrakidis¹,

Jonke²,

Strobl³

et al. 2023

J. Phys. A: Math. Theor.

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We present the construction of the classical Batalin-Vilkovisky action for topological Dirac sigma models. The latter are two-dimensional topological ﬁeld theories that simultaneously generalise the completely gauged Wess-Zumino-Novikov-Witten model and the Poisson sigma model. Their underlying structure is that of Dirac manifolds associated to maximal isotropic and integrable subbundles of an exact Courant algebroid twisted by a 3-form. In contrast to the Poisson sigma model, the AKSZ construction is not applicable for the general Dirac sigma model. We therefore follow a direct approach for determining a suitable BV extension of the classical action functional with ghosts and antiﬁelds satisfying the classical master equation. Special attention is paid on target space covariance, which requires the introduction of two connections with torsion on the Dirac structure.

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“…[27] and extended further in ref. [28] to higher Dirac structures. The underlying reason for the obstruction to QP-ness can be either the presence of a Wess-Zumino term that renders the Q and P structures of the graded manifold incompatible or, more drastically, the very absence of a P structure.…”

Section: Introductionmentioning

confidence: 99%

The BV action of 3D twisted R-Poisson sigma models

Chatzistavrakidis

Ikeda

Šimunić

2022

J. High Energ. Phys.

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We determine the solution to the classical master equation for a 3D topological field theory with Wess-Zumino term and an underlying geometrical structure of a twisted R-Poisson manifold on its target space. The graded geometry of the target space departs from the usual QP structure encountered in the AKSZ construction of topological sigma models, the obstruction being attributed to the presence of the Wess-Zumino 4-form. Due to the inapplicability of the AKSZ construction in this case, we set up the traditional BV/BRST formalism for twisted R-Poisson sigma models in any dimension, which feature an open gauge algebra and constitute multiple stages reducible constrained Hamiltonian systems. An unusual feature of the theories is that they exhibit non-linear openness of the gauge algebra, in other words products of the equations of motion appear in them. Nevertheless, we find the BV action in presence of the 4-form twist in 3D, namely for a specific 4-form twisted (pre-)Courant sigma model. Moreover, we provide a complete set of explicit formulas for the off-shell nilpotent BV operator for untwisted R-Poisson sigma models in any dimension.

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Higher Dimensional Lie Algebroid Sigma Model with WZ Term

Cited by 7 publications

References 50 publications

Basic curvature and the Atiyah cocycle in gauge theory

Basic curvature and the Atiyah cocycle in gauge theory

Topological Dirac sigma models and the classical master equation

The BV action of 3D twisted R-Poisson sigma models

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