# Tropical quantum field theory, mirror polyvector fields, and multiplicities of tropical curves

## TL;DR

This paper develops algebraic structures on polyvector fields of algebraic tori to compute tropical curve multiplicities and explores their connections to mirror symmetry, string topology, and log Gromov-Witten theory.

## Contribution

It introduces a tropical quantum field theory and an $L_{}$-structure on polyvector fields, linking tropical geometry with mirror symmetry and string topology.

## Key findings

- Defined algebraic structures for tropical curve multiplicities
- Connected tropical quantum field theory to mirror symmetry
- Related structures to string topology and gravity algebra

## Abstract

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).

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Source: https://tomesphere.com/paper/1902.07183