Integrability on the Master Space

TL;DR

This paper explores the connection between the Master Space of D3 brane SCFTs at toric Calabi-Yau singularities and integrable systems, revealing a geometric interpretation of the Poisson structure in field theory terms.

Contribution

It introduces a novel geometric framework linking the Master Space to integrable systems, providing new insights into the structure of SCFT moduli spaces.

Findings

The Poisson manifold of the integrable system is reinterpreted through the geometry of the field theory moduli space.

The Master Space acts as a bridge connecting integrability and field theory geometry.

A new geometric perspective on the integrable structure of D3 brane SCFTs is established.

Abstract

It has been recently shown that every SCFT living on D3 branes at a toric Calabi-Yau singularity surprisingly also describes a complete integrable system. In this paper we use the Master Space as a bridge between the integrable system and the underlying field theory and we reinterpret the Poisson manifold of the integrable system in term of the geometry of the field theory moduli space.