Wilson Lines from Representations of NQ-Manifolds

@article{Bonechi2014WilsonLF,
  title={Wilson Lines from Representations of NQ-Manifolds},
  author={Francesco Bonechi and Jian Qiu and Maxim Zabzine},
  journal={International Mathematics Research Notices},
  year={2014},
  volume={2014},
  pages={2440-2493}
}
An NQ-manifold is a non-negatively graded supermanifold with a degree 1 homological vector field. The focus of this paper is to define the Wilson loops/lines in the context of NQ-manifolds and to study their properties. The Wilson loops/lines, which give the holonomy or parallel transport, are familiar objects in usual differential geometry, we analyze the subtleties in the generalization to the NQ-setting and we also sketch some possible applications of our construction. 
View PDF on arXiv
2 Citations

Figures from this paper

2 Citations

Boundary Coupling of Lie Algebroid Poisson Sigma Models and Representations up to Homotopy
A general form for the boundary coupling of a Lie algebroid Poisson sigma model is proposed. The approach involves using the Batalin–Vilkovisky formalism in the AKSZ geometrical version, to write a…
A Construction of Observables for AKSZ Sigma Models
A construction of gauge-invariant observables is suggested for a class of topological field theories, the AKSZ sigma models. The observables are associated to extensions of the target Q-manifold of…

References

SHOWING 1-10 OF 34 REFERENCES
Differential forms on loop spaces and the cyclic bar complex
Quantization of Singular Symplectic Quotients
Some comments on the history, theory, and applicationsof symplectic reduction.- Homology of complete symbols and non-commutative geometry.- Cohomology of the Mumford quotient.- Poisson sigma models…
L_infinity algebras as 1-jets of simplicial manifolds (and a bit beyond)
The procedure "Lie group --> Lie algebra" has a generalization "simplicial manifold --> L_infinity algebra", or yet better, "presheaf on the category of surjective submersions --> L_infinity…
Some title containing the words
Using a basic idea of Sullivan's rational homotopy theory, one can see a Lie groupoid as the fundamental groupoid of its Lie algebroid. This paper studies analogues of Lie algebroids with non-trivial…
Representations up to homotopy of Lie algebroids
Abstract We introduce and study the notion of representation up to homotopy of a Lie algebroid, paying special attention to examples. We use representations up to homotopy to define the adjoint…
AKSZ–BV Formalism and Courant Algebroid-Induced Topological Field Theories
We give a detailed exposition of the Alexandrov–Kontsevich–Schwarz– Zaboronsky superfield formalism using the language of graded manifolds. As a main illustrating example, to every Courant algebroid…
Lie algebroids and homological vector fields
The notion of a Lie algebroid, introduced by J. Pradines, is an analogue of the algebra of a Lie group for differentiable groupoids. Lie algebroids combine the properties of Lie algebras and…
On the structure of graded symplectic supermanifolds and Courant algebroids
This paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudo-Euclidean vector bundles…
Representations up to homotopy and Bott's spectral sequence for Lie groupoids
Graded Manifolds and Drinfeld Doubles for Lie Bialgebroids
We define graded manifolds as a version of supermanifolds endowed with an extra Z-grading in the structure sheaf, called weight (not linked with parity). Examples are ordinary supermanifolds, vector…
...
...