# Off-shell renormalization in the presence of dimension 6 derivative operators. I. General theory

## TL;DR

This paper develops a recursive method for subtracting UV divergences in effective field theories with dimension-6 operators, using homotopy techniques to solve Slavnov-Taylor identities in Abelian gauge theories.

## Contribution

It introduces a systematic approach to off-shell renormalization in theories with dimension-6 derivative operators, employing invariant field coordinates and homotopy methods.

## Key findings

- Successfully solves Slavnov-Taylor identities to all orders
- Disentangles gauge-invariant and gauge-fixing contributions
- Provides a framework adaptable to non-Abelian theories

## Abstract

The consistent recursive subtraction of UV divergences order by order in the loop expansion for spontaneously broken effective field theories with dimension-6 derivative operators is presented for an Abelian gauge group. We solve the Slavnov-Taylor identity to all orders in the loop expansion by homotopy techniques and a suitable choice of invariant field coordinates (named bleached variables) for the linearly realized gauge group. This allows one to disentangle the gauge-invariant contributions to off-shell 1-PI amplitudes from those associated with the gauge-fixing and (generalized) non-polynomial field redefinitions (that do appear already at one loop). The tools presented can be easily generalized to the non-Abelian case.