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We discuss the divergent graviton propagator massless limit problem in $D=26$and show how it can be rigorously approached by interconnecting distinctgauge-fixed Siegel-Zwiebach generating functionals from string theory in thecritical dimension through proper finite-field-dependent BRST (FFBRST)transformations. The massive Fierz-Pauli Lagrangian can be obtained from thegauge-invariant Siegel-Zwiebach one in the unitary gauge as a particular case,however suffering from the van Dam-Veltman-Zakharov discontinuity andpossessing 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 for theSiegel-Zwiebach Lagrangian in the massless limit can be made finite. Gaugeattainability and nilpotent BRST symmetries are explicitly worked out. We writedown the complete corresponding generating functional, including the ghostssector, and construct a convenient FFBRST transformation connecting the unitarygauge to a new bi-parametrized class of gauge-fixings containing the transversetraceless case. By taking into account the corresponding change in the Feynmanintegral Jacobian, a finite massless continuous limit propagator is achievedand fully justified.

Small mass graviton propagator via finite-field-dependent BRST transformations in the critical dimension Siegel-Zwiebach action from string theory