  We introduce algebraic structures on the polyvector fields of an algebraic
torus that serve to compute multiplicities in tropical and log Gromov-Witten
theory while also connecting to the mirror symmetry dual deformation theory of
complex structures. Most notably these structures include a tropical quantum
field theory and an $L_{\infty}$-structure. The latter is an instance of
Getzler's gravity algebra, and the $l_2$-bracket is a restriction of the
Schouten-Nijenhuis bracket. We explain the relationship to string topology in
the appendix (thanks to Janko Latschev).
