Combinatorics

Physics

Electron

Rank (graph theory)

Pure mathematics

Geometry

Compactification (mathematics)

Conjecture

Theoretical physics

Mathematics

Quantum mechanics

Coulomb

Homogeneous space

Journal of High Energy Physics

A bstract According to a conjecture, all 5 d SCFTs should be obtainable by rank- preserving RG flows of 6 d SCFTs compactified on a circle possibly twisted by a background for the discrete global symmetries around the circle. For a 6 d SCFT admitting an F-theory construction, its untwisted compactification admits a dual M-theory description in terms of a “parent” Calabi-Yau threefold which captures the Coulomb branch of the compacti- fied 6 d SCFT. The RG flows to 5 d SCFTs can then be identified with a sequence of flop transitions and blowdowns of the parent Calabi-Yau leading to “descendant” Calabi-Yau threefolds which describe the Coulomb branches of the resulting 5 d SCFTs. An explicit description of parent Calabi-Yaus is known for untwisted compactifications of rank one 6 d SCFTs. In this paper, we provide a description of parent Calabi-Yaus for untwisted compactifications of arbitrary rank 6 d SCFTs. Since 6d SCFTs of arbitrary rank can be viewed as being constructed out of rank one SCFTs, we accomplish the extension to arbi- trary rank by identifying a prescription for gluing together Calabi-Yaus associated to rank one 6d SCFTs.

Classifying 5d SCFTs via 6d SCFTs: arbitrary rank