Tropical Quantum Field Theory, Mirror Polyvector Fields, and Multiplicities of Tropical Curves

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