Characteristic classes of Q-manifolds: Classification and applications

S. L. Lyakhovich, E. A. Mosman, A. A. Sharapov

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A Q-manifold M is a supermanifold endowed with an odd vector field Q squaring to zero. The Lie derivative LQ along Q makes the algebra of smooth tensor fields on M into a differential algebra. In this paper, we define and study the invariants of Q-manifolds called characteristic classes. These take values in the cohomology of the operator LQ and, given an affine symmetric connection with curvature R, can be represented by universal tensor polynomials in the repeated covariant derivatives of Q and R up to some finite order. As usual, the characteristic classes are proved to be independent of the choice of the affine connection used to define them. The main result of the paper is a complete classification of the intrinsic characteristic classes, which, by definition, do not vanish identically on flat Q-manifolds. As an illustration of the general theory we interpret some of the intrinsic characteristic classes as anomalies in the BV and BFV-BRST quantization methods of gauge theories. An application to the theory of (singular) foliations is also discussed.

Original languageEnglish
Pages (from-to)729-759
Number of pages31
JournalJournal of Geometry and Physics
Volume60
Issue number5
DOIs
Publication statusPublished - May 2010
Externally publishedYes

Fingerprint

Characteristic Classes
Tensor
differential algebra
tensors
Singular Foliation
Lie Derivative
Supermanifold
Affine Connection
Differential Algebra
Covariant Derivative
homology
Gauge Theory
Anomaly
gauge theory
Cohomology
Vanish
Quantization
Vector Field
polynomials
algebra

Keywords

  • Characteristic classes
  • Gauge theories
  • Q-manifolds

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

Cite this

Characteristic classes of Q-manifolds : Classification and applications. / Lyakhovich, S. L.; Mosman, E. A.; Sharapov, A. A.

In: Journal of Geometry and Physics, Vol. 60, No. 5, 05.2010, p. 729-759.

Research output: Contribution to journalArticle

Lyakhovich, S. L. ; Mosman, E. A. ; Sharapov, A. A. / Characteristic classes of Q-manifolds : Classification and applications. In: Journal of Geometry and Physics. 2010 ; Vol. 60, No. 5. pp. 729-759.
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