String networks as tropical curves

TL;DR

This paper links (p,q)-string networks in supergravity to tropical curves, revealing a geometric perspective that connects amoebas, Ronkin functions, and dyon counting in M-theory.

Contribution

It introduces a novel geometric framework for supergravity solutions of string networks using tropical geometry and amoebas, expanding the understanding of their mathematical structure.

Findings

Networks correspond to tropical curves as amoeba spines

Kaehler potential identified with Ronkin function

Implications for counting dyons in M-theory

Abstract

A prescription for obtaining supergravity solutions for planar (p,q)-string networks is presented, based on earlier results. It shows that networks may be looked upon as tropical curves emerging as the spine of the amoeba of a holomorphic curve in M-theory. The Kaehler potential of supergravity is identified with the corresponding Ronkin function. Implications of this identification in counting dyons is discussed.