Basic curvature & the Atiyah cocycle in gauge theory

Chatzistavrakidis, Athanasios; Jonke, Larisa (2024) Basic curvature & the Atiyah cocycle in gauge theory. Journal of Physics A: Mathematical and Theoretical, 57 (46). ISSN 1751-8113

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Abstract

Motivated from target space covariant formulations of topological sigma models and from a graded-geometric approach to higher gauge theory, we study connections on Lie and Courant algebroids and on their description as differential graded (dg) manifolds. We revisit the notion of basic curvature for a connection on a Lie algebroid, which measures its compatibility with the Lie bracket and it appears in the BV-BRST differential of 2D gauge theories such as (twisted) Poisson and Dirac sigma models. We define a basic curvature tensor for connections on Courant algebroids and we show that in the description of a Courant algebroid as a QP2 manifold it appears naturally as part of the homological vector field together with the Gualtieri torsion of an induced generalised connection. Furthermore, we consider connections on dg manifolds and revisit the structure of gauge transformations in the graded-geometric approach to higher gauge theories from a manifestly covariant perspective. We argue that it is governed by the brackets of a Kapranov L∞ algebra, whose binary bracket is given by the Atiyah cocycle that measures the compatibility of the connection with the homological vector field. We also revisit some aspects of the derived bracket construction and show how to extend it to connections and tensors.

Item Type:	Article
Additional Information:	‘This is the version of the article before peer review or editing, as submitted by an author to Journal of Physics A: Mathematical and Theoretical.  IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it.  The Version of Record is available online at https://iopscience.iop.org/article/10.1088/1751-8121/ad88c0’
Uncontrolled Keywords:	algebroids; Atiyah cocycle; basic curvature
Subjects:	NATURAL SCIENCES > Physics
Divisions:	Theoretical Physics Division
Projects:	Project title Project leader Project code Project type Simetrije u kvantnoj gravitaciji-SYMM4QG Larisa Jonke IP-2019-04-4168 HRZZ
Depositing User:	Larisa Jonke
Date Deposited:	16 Dec 2025 15:46
URI:	http://fulir.irb.hr/id/eprint/10548
DOI:	10.1088/1751-8121/ad88c0

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