On classical and quantum deformations of gauge theories

We elaborate the generalizations of the approach to gauge-invariant deformations of the gauge theories developed in our previous work (Buchbinder and Lavrov in JHEP 06:097, 2021). In the given paper we construct the exact transformations defying the gauge-invariant deformed theory on the base of initial gauge theory with irreducible open gauge algebra. Like in [1], for the theories with open gauge algebras these transformations are the shifts of the initial gauge fields $$A \rightarrow A+h(A)$$A → A + h ( A ) , with the help of the arbitrary and in general non-local functions h(A). The results are applied to study the quantum aspects of the deformed theories. We derive the exact relation between the quantum effective actions for the above classical theories, where one is obtained from another with the help of the deformation.