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

Chatzistavrakidis, Athanasios; Ikeda, Noriaki; Šimunić, Grgur

doi:10.1007/jhep10(2022)002

Cited by 8 publications

(7 citation statements)

References 43 publications

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“…What is more, the above arguments are not only relevant for 2D AKSZ and beyond AKSZ topological field theories, but also in higher dimensions. In 3D, the Courant sigma model once again leads to a BV action whose 4-fermion term corresponds when covariantized to a basic curvature tensor, this time for connections on Courant algebroids [30,31]. Here we give a general definition of such a tensor, 1 in other words from a field-theoretical perspective we answer the question: Is there a unifying framework where the curvature and basic curvature tensors that multiply 4-fermion terms find a common origin through a suitable curvature tensor on a Courant algebroid?…”

Section: Motivationmentioning

confidence: 99%

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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: Motivationmentioning

confidence: 99%

“…This completes the derivation of the full, off-shell nilpotent BV operator for the Poisson sigma model. We are now ready to reexamine it from a target space covariant perspective, following and extending the analysis of [28] and [30], which was not performed for the BV operator.…”

Section: Poisson Sigma Model and Basic Curvaturementioning

confidence: 99%

Basic curvature and the Atiyah cocycle in gauge theory

Chatzistavrakidis¹,

Jonke²

2023

Preprint

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“…Such 4-form-twisted Courant sigma models were considered before in [13], but their BV action has not been studied. In our approach, this is fully addressed and the BV action can be found, at least in the twisted R-Poisson subclass of twisted Courant sigma models [14].…”

Section: Athanasios Chatzistavrakidismentioning

confidence: 99%

“…One interesting outcome is that all ghosts in the 𝜓-series, save the highest, receive equation of motion corrections. This strategy was developed recently in [14] and it led to complete closed expressions for the BV operator, from which the BV action can be fully determined. We refer to the original paper for a detailed discussion.…”

Section: Pos(corfu2021)271mentioning

confidence: 99%

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Twisted R-Poisson Sigma Models

Chatzistavrakidis¹

2022

Proceedings of Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2021)

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The AKSZ construction was developed as a geometrical formalism to find the solution to the classical master equation in the BV quantization of topological branes based on the concept of QP manifolds. However, the formalism does not apply in presence of Wess-Zumino terms, as demonstrated recently by Ikeda and Strobl in the simplest example of WZW-Poisson sigma models. In this contribution, we review a class of topological field theories in arbitrary dimensions, the twisted R-Poisson sigma models, which suitably generalize Poisson or twisted Poisson sigma models. Their relation to differential graded manifolds and higher geometry is discussed and we sketch how to identify the solution to the classical master equation even though the target space does not have a QP structure.

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Drinfel’d double of bialgebroids for string and M theories: dual calculus framework

Çatal-Özer,

Doğan,

Yetişmişoğlu

2024

J. High Energ. Phys.

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We extend the notion of Lie bialgebroids for more general bracket structures used in string and M theories. We formalize the notions of calculus and dual calculi on algebroids. We achieve this by reinterpreting the main results of the matched pairs of Leibniz algebroids. By examining a rather general set of fundamental algebroid axioms, we present the compatibility conditions between two calculi on vector bundles which are not dual in the usual sense. Given two algebroids equipped with calculi satisfying the compatibility conditions, we construct its double on their direct sum. This generalizes the Drinfel’d double of Lie bialgebroids. We discuss several examples from the literature including exceptional Courant brackets. Using Nambu-Poisson structures, we construct an explicit example, which is important both from physical and mathematical point of views. This example can be considered as the extension of triangular Lie bialgebroids in the realm of higher Courant algebroids, that automatically satisfy the compatibility conditions. We extend the Poisson generalized geometry by defining Nambu-Poisson exceptional generalized geometry and prove some preliminary results in this framework. We also comment on the global picture in the framework of formal rackoids and we slightly extend the notion for vector bundle valued metrics.

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

Cited by 8 publications

References 43 publications

Basic curvature and the Atiyah cocycle in gauge theory

Basic curvature and the Atiyah cocycle in gauge theory

Twisted R-Poisson Sigma Models

Drinfel’d double of bialgebroids for string and M theories: dual calculus framework

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