Functional BRST-invariant approach to the Siegel-Zwiebach symmetric rank-two tensor action in the critical dimension – massive gravity clues from string theory

Abstract

We discuss the rank-two tensorial Siegel-Zwiebach action from string field theory within a BRST-invariant functional framework in the bosonic critical dimension. We obtain a new family of generalized proper gauge-fixing conditions. Gauge attainability and all corresponding nillpotent BRST symmetries are explicitly worked out. Finite-field-dependent BRST transformations (FFBRST) are shown to connect the effective ghost-dependent actions in different gauges. The massive Fierz-Pauli Lagrangian can be obtained from the gauge-invariant Siegel-Zwiebach one in the unitary gauge as a particular case, however, due to the well-known van Dam-Veltman-Zakharov (vDVZ) discontinuity, possessing a ill-defined propagator in the massless limit. Nevertheless, alternatively working in a more suitable generalized Lorenz type gauge, including the transverse-traceless case, the graviton propagator within the Siegel-Zwiebach Lagrangian context can be made finite in the massless limit. We write down the complete Green's functions generating functional, including the auxiliary fields and ghosts sectors. By taking into account the corresponding change in the Feynman integral Jacobian, we construct a convenient FFBRST transformation connecting the unitary gauge to a new bi-parametrized class of gauge-fixings containing the transverse-traceless case.