Ward Identities for the Standard Model Effective Field Theory.

We derive Ward identities for the Standard Model Effective Field Theoryusing the background field method. The resulting symmetry constraints on the Standard Model Effective Field Theoryare basis independent, and constrain the perturbative and power-counting expansions. A geometric description of the field connections, and real representationsfor the $\rm SU(2)_L \times U(1)_Y$ generators, underlies the derivation.