The hitchhiker's guide to 4d $\mathcal{N}=2$ superconformal field theories

Abstract

Superconformal field theory with \mathcal{N}=2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mstyle mathvariant="script"> <mml:mi>𝒩</mml:mi> </mml:mstyle> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> supersymmetry in four dimensional spacetime provides a prime playground to study strongly coupled phenomena in quantum field theory. Its rigid structure ensures valuable analytic control over non-perturbative effects, yet the theory is still flexible enough to incorporate a large landscape of quantum systems. Here we aim to offer a guidebook to fundamental features of the 4d \mathcal{N}=2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mstyle mathvariant="script"> <mml:mi>𝒩</mml:mi> </mml:mstyle> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> superconformal field theories and basic tools to construct them in string/M-/F-theory. The content is based on a series of lectures at the Quantum Field Theories and Geometry School in July 2020.