Equivariant Higher Hochschild Homology and Topological Field Theories

We present a version of higher Hochschild homology for spaces equipped with principal bundles for a structure group $G$. As coefficients, we allow $E_\infty$-algebras with $G$-action. For this homology theory, we establish an equivariant version of excision and prove that it extends to an equivariant topological field theory with values in the $(\infty,1)$-category of cospans of $E_\infty$-algebras.
Comment: 26 pages, 2 figures, minor changes, comparison to equivariant factorization homology added; accepted for publication in "Homology, Homotopy and Applications"