Abstract
We initiate the systematic investigation of non-flat resolutions of non-minimal singularities in elliptically fibered Calabi-Yau threefolds. Compactification of M-theory on these geometries provides an alternative approach to studying phases of five-dimensional superconformal field theories (5d SCFTs). We argue that such resolutions capture non-trivial holonomies in the circle reduction of the 6d conformal matter theory that is the F-theory interpretation of the singular fibration. As these holonomies become mass deformations in the 5d theory, non-flat resolutions furnish a novel method in the attempt to classify 5d SCFTs through 6d SCFTs on a circle. A particularly pleasant aspect of this proposal is the explicit embedding of the 5d SCFT’s enhanced flavor group inside that of the parent 6d SCFT, which can be read off from the geometry. We demonstrate these features in toric examples which realize 5d theories up to rank four.
Highlights
Renormalization group (RG) flows triggered by mass deformations connect different 5d N = 1 supersymmetric gauge theories
Compactification of M-theory on these geometries provides an alternative approach to studying phases of five-dimensional superconformal field theories (5d SCFTs)
We argue that such resolutions capture nontrivial holonomies in the circle reduction of the 6d conformal matter theory that is the F-theory interpretation of the singular fibration
Summary
To make sense of them in F-theory compactifications to 6d, one can blow-up the base B2 at the point p This procedure introduces a collection of rational curves Σi ⊂ B2 in the blown-up base, over which the (pulled-back) elliptic fibration π : Y3 → B2 only has minimal singularities, i.e., ordinary gauge algebras gi and matter representations. If Σi carries singular fibers, i.e., supports a gauge theory, its squared gauge coupling is proportional to vol(Σi)−1 Blowing down these curves, reproducing the non-minimal singularity, we immediately see that the gauge coupling becomes formally infinite. Some 6d SCFTs can arise solely from a singular point p of the base, without colliding codimension one singularities [18] These SCFTs typically have no global symmetries. These theories are called 6d conformal matter theories and are important building blocks of 6d SCFTs
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