BRST-BV Quantum Actions for Constrained Totally-Symmetric Integer HS Fields

Abstract

A constrained BRST-BV Lagrangian formulation for totally symmetric massless HS fields in a $d$-dimensional Minkowski space is extended to a non-minimal constrained BRST-BV Lagrangian formulation by using a non-minimal BRST operator $Q_{c|\mathrm{tot}}$ with non-minimal Hamiltonian BFV oscillators $\overline{C},\overline{\mathcal{P}},\lambda ,\pi$, as well as antighost and Nakanishi-Lautrup tensor fields, in order to introduce an admissible self-consistent gauge condition. The gauge-fixing procedure involves an operator gauge-fixing BRST-BFV Fermion ${\Psi }_H$ as a kernel of the gauge-fixing BRST-BV Fermion functional $\Psi$, manifesting the concept of BFV-BV duality. A Fock-space quantum action with non-minimal BRST-extended off-shell constraints is constructed as a shift of the total generalized field-antifield vector by a variational derivative of the gauge-fixing Fermion $\Psi$ in a total BRST-BV action $S_{0|s}^{\Psi }=\int d{\eta }_0⟨{\chi }_{\mathrm{tot}|c}^{\Psi 0}\left|Q_{c|\mathrm{tot}}\right|{\chi }_{\mathrm{tot}|c}^{\Psi 0}⟩$. We use a gauge condition which depends on two gauge parameters, thereby extending the case of $R_{\xi }$-gauges. For triplet and duplet formulations we explored the representations with only traceless field-antifield and source variables. For the generating functionals of Green's functions, BRST symmetry transformations are suggested and Ward identities are obtained.

arXiv comment21 pages, no figures, typos corrected; footnote on interacting terms, remark on double-traceless field representation for correct path integral with Eqs. (90)-(93), representation for quantum BV action, path integral for cubic vertex with Eqs.(97)-(101) and 1 reference added; conclusion improved; published version in Nucl. Phys. B

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• Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields
• BRST-BV approach for interacting higher spin fields
• Towards the structure of a cubic interaction vertex for massless integer higher spin fields
• Gauge Invariant Lagrangian Formulations for Mixed Symmetry Higher Spin Bosonic Fields in AdS Spaces
• Higher-Spin Gauge Models in the BRST-antifield Formalism