Mastering the Master Space

TL;DR

This paper explores the concept of the master space in supersymmetric gauge theories, especially in D-brane world-volume theories, revealing its role in understanding moduli spaces, symmetries, and physical phenomena.

Contribution

It provides a detailed analysis of the properties of the master space and extends the understanding of its role in gauge theories with multiple branes using the plethystic program.

Findings

Master space encodes Higgsing and BPS spectra.

Properties of the master space relate to hidden symmetries.

Analysis extends to multiple branes using plethystic techniques.

Abstract

Supersymmetric gauge theories have an important but perhaps under-appreciated notion of a master space, which controls the full moduli space. For world-volume theories of D-branes probing a Calabi-Yau singularity X the situation is particularly illustrative. In the case of one physical brane, the master space F is the space of F-terms and a particular quotient thereof is X itself. We study various properties of F which encode such physical quantities as Higgsing, BPS spectra, hidden global symmetries, etc. Using the plethystic program we also discuss what happens at higher number N of branes. This letter is a summary and some extensions of the key points of a longer companion paper arXiv:0801.1585.