Abstract
Algebraic properties of the BRST symmetry associated to the twisted gauge symmetry occurring in the $\kappa$-Poincar\'e invariant gauge theories on the $\kappa$-Minkowski space are investigated. We find that the BRST operation associated to the gauge invariance of the action functional can be continuously deformed together with its corresponding Leibniz rule, into a nilpotent twisted BRST operation, leading to a twisted BRST symmetry algebra which may be viewed as a noncommutative analog of the usual Yang-Mills BRST algebra.
Highlights
Some attention has been paid to noncommutative field theories (NCFTs) on κ-Minkowski spaces for more than two decades; see e.g., [1,2,3,4] and references therein
We find that the BRST operation associated to the gauge invariance of the action functional can be continuously deformed together with its corresponding Leibniz rule, into a nilpotent twisted BRST operation, leading to a twisted BRST symmetry algebra which may be viewed as a noncommutative analog of the usual Yang-Mills BRST algebra
The BRST symmetry is essential in topological field theories [33] of cohomological class to perform a suitable gauge fixing [34] as well as in the determination of the corresponding invariants. This applies to the Donaldson invariants [35] stemming from the four-dimensional topological Yang-Mills theory [36] as well as the invariants related to the two-dimensional topological gravity [37], where in each case the use of a suitable BRST symmetry was shown [38] to be essential to characterize the relations between the different schemes describing the equivariant cohomology [39] relevant to these theories
Summary
Some attention has been paid to noncommutative field theories (NCFTs) on κ-Minkowski spaces for more than two decades; see e.g., [1,2,3,4] and references therein. We have taken advantage of the convenient star product used in [3] to characterize the classical properties of κ-Poincareinvariant gauge theories on κ-Minkowski spaces [16]. In [16], we have shown that the modular twist effect can be entirely neutralized, leading to a κ-Poincareinvariant and gauge invariant functional action with physically acceptable commutative limit, provided the κ-Minkowski space is five dimensional.. In [16], we have shown that the modular twist effect can be entirely neutralized, leading to a κ-Poincareinvariant and gauge invariant functional action with physically acceptable commutative limit, provided the κ-Minkowski space is five dimensional.4 This can be achieved thanks to the existence of a unique twisted noncommutative differential calculus based on a family of twisted derivations of.
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