Towards the classification of rank-$r$ $\mathcal{N}=2$ SCFTs. Part I: twisted partition function and central charge formulae

Abstract

We derive explicit formulae to compute the $a$ and $c$ central charges of four dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $\mathcal{N}=2$ SCFTs which culminate with our $\mathcal{N}=2$ UV-IR simple flavor condition. This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $\mathcal{N}=2$ SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper.

arXiv comment30 pages, submitted to JHEP

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Cited by in corpus (16)

• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• Magnetic quivers for rank 2 theories
• S-folds, String Junctions, and 4D $\mathcal{N}=2$ SCFTs
• Fibrations and Hasse diagrams for 6d SCFTs
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs
• On the compactification of 5d theories to 4d
• Cutting and gluing with running couplings in $\mathcal{N}=2$ QCD
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• A new rank-2 Argyres-Douglas theory
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Exceptional moduli spaces for exceptional $\mathcal{N}=3$ theories
• Symmetric Orbifold Theories from Little String Residues
• Disconnected gauge groups in the infrared
• Completely (iso-)split scale-invariant Coulomb branch geometries are isotrivial