A Tropical Look at Coisotropic Branes and Quantization

TL;DR

This paper explores the tropicalization of topological sigma models with boundaries, revealing a natural decomposition of A-branes into tropical Lagrangian and coisotropic branes, and demonstrates their use in quantizing symplectic manifolds.

Contribution

It introduces a tropical perspective on branes in sigma models, explicitly constructs tropical branes, and applies this framework to quantize symplectic manifolds.

Findings

Tropical limit decomposes A-branes into two classes.

Explicit construction of tropical Lagrangian and coisotropic branes.

Application of tropical branes to quantize symplectic manifolds.

Abstract

We continue our investigation of tropical branes by exploring the tropicalization of topological sigma models with boundaries. We show that the tropical limit naturally decomposes conventional A-branes into two distinct classes: tropical Lagrangian branes and tropical coisotropic branes. By carefully analyzing the modified boundary conditions emerging from the tropological sigma models, we construct these tropical branes explicitly and demonstrate their utility in an example where we quantize a symplectic manifold through the use of a tropical version of brane quantization.