Geometric approach to BRST-symmetry and ZN-generalization of superconnection

DOI

10.2991/jnmp.2006.13.s.2How to use a DOI?

Abstract

We propose a geometric approach to the BRST-symmetries of the Lagrangian of a topological quantum field theory on a four dimensional manifold based on the formalism of superconnections. Making use of a graded q-differential algebra, where q is a primitive N-th root of unity, we also propose a notion of ZN -connection which is a generalization of a superconnection. In our approach the Lagrangian of a topological field theory is presented as the value of the curvature of a superconnection evaluated at an appropriate section of a vector bundle. Since this value of the curvature satisfies the Bianchi identity and representing the Bianchi identity in this case in the form of an operator applied to the mentioned above value of the curvature we obtain an operator which gives zero when applied to the Lagrangian. We show that this operator generates the BRST-transformations of the fields of a topological field theory on a four dimensional manifold.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - V. Abramov
AU  - O. Liivapuu
PY  - 2006
DA  - 2006/08/01
TI  - Geometric approach to BRST-symmetry and ZN-generalization of superconnection
JO  - Journal of Nonlinear Mathematical Physics
SP  - 9
EP  - 20
VL  - 13
IS  - Supplement
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2006.13.s.2
DO  - 10.2991/jnmp.2006.13.s.2
ID  - Abramov2006
ER  -