Aspects of 4d supersymmetric dynamics and geometry

TL;DR

This paper provides an overview of the geometric methods used to analyze four-dimensional supersymmetric quantum field theories, emphasizing strong coupling phenomena like duality and symmetry emergence.

Contribution

It reviews existing literature and introduces some unpublished derivations on geometric engineering of 4D supersymmetric models from 6D SCFTs.

Findings

Geometric engineering links 4D supersymmetric theories to 6D SCFTs.

Strong coupling phenomena are naturally embedded in geometric constructions.

The paper consolidates known results with new derivations.

Abstract

In this set of five lectures we present a basic toolbox to discuss the dynamics of four dimensional supersymmetric quantum field theories. In particular we overview the program of geometrically engineering the four dimensional supersymmetric models as compactifications of six dimensional SCFTs. We discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be naturally imbedded in the geometric constructions. The lectures mostly review results which previously appeared in the literature but also contain some unpublished derivations.