Characteristic classes of Q-manifolds: Classification and applications

Characteristic classes of Q-manifolds: Classification and applications

Bibliographic Details
Parent link:Journal of Geometry and Physics: Scientific Journal
Vol. 60, iss. 5.— 2010.— [P. 729–759]
Main Author: Lyakhovich S. L.
Other Authors: Mosman E. A. Elena Arkadievna, Sharapov A. A.
Summary:Title screen
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.
Режим доступа: по договору с организацией-держателем ресурса
Language:English
Published: 2010
Subjects:
электронный ресурс
труды учёных ТПУ
Q-manifolds
Characteristic classes
Gauge theories
Online Access:http://dx.doi.org/10.1016/j.geomphys.2010.01.008
Format: Electronic Book Chapter
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=642067

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