Lagrangian Sp(3) BRST symmetry for irreducible gauge theories (Q2746653)

The authors show that the methods of homological perturbation theory can be extended in order to cover the construction of the Lagrangian Sp(3) BRST symmetry in the irreducible case. This is done by triplicating each differential appearing in the antibracket-antifield BRST formalism. The correct ghost spectrum is determined by the triplication of the gauge transformations of a given irreducible theory. Then a proper construction of the exterior longitudinal tricomplex is developed to ensure that the cohomologies associated with each of the three exterior longitudinal derivatives are isomorphic to the cohomology of the standard exterior longitudinal derivative along the gauge orbits from the BRST description of the initial irreducible theory. It is shown that the canonical generator of the Sp(3) BRST algebra, which is a solution to the classical master equation of the Sp(3) formalism, exists. Finally a gauge-fixing procedure providing the invariance of the effective action with respect to BRST symmetries is constructed.