Volume 13, Issue Supplement, August 2006, Pages 9 - 20
Geometric approach to BRST-symmetry and ZN-generalization of superconnection
- V ABRAMOV, O LIIVAPUU
- Corresponding Author
- V ABRAMOV
Available Online 1 August 2006.
- https://doi.org/10.2991/jnmp.2006.13.s.2How to use a DOI?
- 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.
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Cite this article
TY - JOUR AU - V ABRAMOV AU - O LIIVAPUU PY - 2006 DA - 2006/08 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 - https://doi.org/10.2991/jnmp.2006.13.s.2 ID - ABRAMOV2006 ER -