Abstract

An E_1 Calabi-Yau object A in a symmetric monoidal infinity-category C is a dualizable E_1 algebra together with an S^1-cyclic trace that exhibits a self duality of A. Examples include the cochain complex of any closed oriented manifold. By work of Barkan and Steinebrunner, every E_1 Calabi-Yau object in C defines a 2-dimensionsional “open” field theory with values in C, which are symmetric monoidal functors from the open 2-bordism category O to C. In upcoming work with Barkan and Steinebrunner, we show that any open field theory F extends canonically to an open-closed field theory whose value at the circle is the THH of the E_1 Calabi-Yau object A associated to F. As a corollary, we obtain an action of the moduli spaces of surfaces on the THH of E_1 Calabi-Yau algebras. This provides a space level refinement of previous work of Costello (over Q) and Wahl (over Z).