Ward Identities for the Standard Model Effective Field Theory

We derive Ward identities for the Standard Model Effective Field Theory using the background field method. The resulting symmetry constraints on the Standard Model Effective Field Theory are basis independent, and constrain the perturbative and power-counting expansions. A geometric description of the field connections, and real representations for the $\mathrm{S}\mathrm{U}(2{)}_{\mathrm{L}}\times \mathrm{U}(1{)}_{\mathrm{Y}}$ generators, underlies the derivation.