Gauge invariant perturbation theory via homotopy transfer

A bstract We show that the perturbative expansion of general gauge theories can be expressed in terms invariant variables to all orders perturbations. In this we generalize techniques developed cosmological perturbation theory, using Bardeen variables, by interpreting passing over fields as a homotopy transfer strongly Lie algebras encoding theory. This is illustrated for Yang-Mills gravity on flat and backgrounds massless sector closed string The lemma yields an algorithmic procedure determine higher corrections action these.