Portal de Periódicos da CAPES

Homological classification of 4d $$ \mathcal{N} $$ = 2 QFT. Rank-1 revisited

2019; Springer Nature; Volume: 2019; Issue: 10 Linguagem: Inglês

10.1007/jhep10(2019)013

1127-2236

Matteo Caorsi, Sergio Cecotti,

Algebraic Geometry and Number Theory

A bstract Argyres and co-workers started a program to classify all 4d $$ \mathcal{N} $$ N = 2 QFT by classifying Special Geometries with appropriate properties. They completed the program in rank-1. Rank-1 $$ \mathcal{N} $$ N = 2 QFT are equivalently classified by the Mordell-Weil groups of certain rational elliptic surfaces. The classification of 4d $$ \mathcal{N} $$ N = 2 QFT is also conjectured to be equivalent to the representation theoretic (RT) classification of all 2-Calabi-Yau categories with suitable properties. Since the RT approach smells to be much simpler than the Special-Geometric one, it is worthwhile to check this expectation by reproducing the rank-1 result from the RT side. This is the main purpose of the present paper. Along the route we clarify several issues and learn new details about the rank-1 SCFT. In particular, we relate the rank-1 classification to mirror symmetry for Fano surfaces. In the follow-up paper we apply the RT methods to higher rank 4d $$ \mathcal{N} $$ N = 2 SCFT.