Abstract
According to a conjecture, all 5d SCFTs should be obtainable by rank- preserving RG flows of 6d SCFTs compactified on a circle possibly twisted by a background for the discrete global symmetries around the circle. For a 6d 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 6d SCFT. The RG flows to 5d 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 5d SCFTs. An explicit description of parent Calabi-Yaus is known for untwisted compactifications of rank one 6d SCFTs. In this paper, we provide a description of parent Calabi-Yaus for untwisted compactifications of arbitrary rank 6d 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.
Highlights
Following a recent proposal [1], a strategy for classifying 5d SCFTs in terms of6d SCFTs was spelled out in [3]
We provide a description of parent Calabi-Yaus for untwisted compactifications of arbitrary rank 6d SCFTs
We describe the construction of Mori cone MiC of the surface surface without the blowups as (SCi) with the blowups included
Summary
Following a recent proposal [1] (see [2]), a strategy for classifying 5d SCFTs in terms of. SR1 of radius R and let us turn on generic holonomies for the continuous gauge and global symmetries of T around SR1 This corresponds to compactifying F-theory on XT × SR1 and turning on holonomies on the 7-branes around SR1. For the KK theories TKK that we discussed above, such RG flows are described by a sequence of flop transitions and blowdowns on XT generating new smooth non-compact Calabi-Yau threefolds that do not admit an elliptic fibration. In this sense, one can regard XT as “parent” Calabi-Yaus and the Calabi-Yaus obtained after flops and blowdowns as their “descendant” Calabi-Yaus. In appendix A, we provide instructions on using the mathematica notebook “Pushforward.nb” attached as supplementary material to this paper
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