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Snowmass White Paper on SCFTs

Philip C. Argyres, Jonathan J. Heckman, Kenneth Intriligator, Mario Martone

TL;DR

This Snowmass white paper surveys the landscape of SCFTs in $3\le D\le 6$, outlining the status of classification across dimensions and the deep links between physics and mathematics. It highlights how higher-D SCFTs emerge from string/M-/F-theory constructions and how lower-D theories are engineered via compactifications and dualities, with substantial interplay with geometry, nilpotent orbits, and vertex operator algebras. The work also discusses extended operators and higher-form symmetries, and addresses theories with less supersymmetry, emphasizing open problems and future directions. Overall, it provides a comprehensive roadmap connecting SCFT classification, mathematical structures, and symmetry frameworks across dimensions, guiding future research at the interface of QFT and mathematics.

Abstract

Superconformal field theories (SCFTs) occupy a central role in the study of many aspects of quantum field theory. In this white paper for the Snowmass process we give a brief overview of aspects of SCFTs in $3\leq D \leq 6$ space-time dimensions, including classification efforts and some of the vast current research trends on the physical and mathematical structures generated by this rich class of physical theories.

Snowmass White Paper on SCFTs

TL;DR

This Snowmass white paper surveys the landscape of SCFTs in , outlining the status of classification across dimensions and the deep links between physics and mathematics. It highlights how higher-D SCFTs emerge from string/M-/F-theory constructions and how lower-D theories are engineered via compactifications and dualities, with substantial interplay with geometry, nilpotent orbits, and vertex operator algebras. The work also discusses extended operators and higher-form symmetries, and addresses theories with less supersymmetry, emphasizing open problems and future directions. Overall, it provides a comprehensive roadmap connecting SCFT classification, mathematical structures, and symmetry frameworks across dimensions, guiding future research at the interface of QFT and mathematics.

Abstract

Superconformal field theories (SCFTs) occupy a central role in the study of many aspects of quantum field theory. In this white paper for the Snowmass process we give a brief overview of aspects of SCFTs in space-time dimensions, including classification efforts and some of the vast current research trends on the physical and mathematical structures generated by this rich class of physical theories.
Paper Structure (12 sections)

This paper contains 12 sections.

Table of Contents

  1. Background and Motivation
  2. Organization
  3. Classification
  4. 6D SCFTs
  5. 5D SCFTs
  6. 4D ${\mathcal{N}}\geq 2$ SCFTs
  7. 3D ${\mathcal{N}}\geq 4$ SCFTs
  8. SCFTs and new mathematics
  9. Geometry and singularities
  10. Vertex operator algebras
  11. Extended operators and higher-form symmetries
  12. Theories with less supersymmetry ($8>N_Q\geq 2$)