I was reading John D.S. Jones' paper "Cyclic homology and equivariant homology" where he introduces a variant of cyclic homology that is isomorphic (as modules over the ring $K[u]$) to equivariant homology of the loop space of a simply connected space with the $S^1$ action on the loops, which is what I mean by String Homology.

I have seen how the loop homology BV operator shows up in Hochschild homology. Do we have an analog of string topology operations, such as the string bracket, in cyclic homology?