Morse functions and Real Lagrangian Thimbles on Adjoint Orbits

TL;DR

This paper explores the relationship between Lagrangian thimbles in Landau-Ginzburg models and Morse theory on real parts, specifically focusing on models derived from Lie theory and their explicit constructions.

Contribution

It provides an explicit construction of real Lagrangian thimbles for Lie-theoretic Landau-Ginzburg models and compares them to Morse-theoretic stable and unstable manifolds.

Findings

Explicit constructions of real Lagrangian thimbles

Comparison with Morse stable and unstable manifolds

Insights into the geometry of Landau-Ginzburg models

Abstract

We compare Lagrangian thimbles for the potential of a Landau-Ginzburg model to the Morse theory of its real part. We explore Landau-Ginzburg models defined using Lie theory, constructing their real Lagrangian thimbles explicitly and comparing them to the stable and unstable manifolds of the real gradient flow.