Off-shell renormalization of spontaneously broken effective gauge theories

Abstract

The off-shell renormalization of spontaneously broken effective gauge theories is carried out following the Algebraic Renormalization approach. We provide a constructive way to obtain the canonical transformations with respect to the Batalin-Vilkovisky bracket, associated with the gauge group of the theory, that generalize the familiar linear field redefinitions arising in power-counting renormalizable theories. By taking into account such generalized field redefinitions one can consistently extract the $\beta$-functions of the higher dimensional operators order by order in the loop expansion. The gauge invariance of the ultraviolet coefficients for physical operators is explicitly checked at one loop order.