On gauge-invariant deformation of reducible gauge theories

New method for construction of gauge-invariant deformed theory from an initial gauge theory proposed in our previous papers (Buchbinder and Lavrov in JHEP 06:854, 2021; Buchbinder and Lavrov in Eur Phys J C 81:856, 2021) for closed/open gauge algebras is extended to the case of reducible gauge algebras. The deformation procedure is explicitly described with the help of generating functions of anticanonical transformations depending on fields of the initial gauge action only. The deformed gauge-invariant action and the deformed gauge generators are described with the help of the generating functions in a closed and simple form. As an example of reducible gauge systems we consider the free fermionic p-form fields or, in another words, the antisymmetric tensor-spinor fields. It is proved that gauge-invariant deformation of fermionic p-form fields leads always to non-local deformed theory which does not contain a closed local sector. In its turn the model based on two fermionic 2-form fields and a real massive scalar field admits local interactions between these fields in local sector of the deformed action