Abstract
Starting from 6D superconformal field theories (SCFTs) realized via F-theory, we show how reduction on a circle leads to a uniform perspective on the phase structure of the resulting 5D theories, and their possible conformal fixed points. Using the correspon-dence between F-theory reduced on a circle and M-theory on the corresponding elliptically fibered Calabi-Yau threefold, we show that each 6D SCFT with minimal supersymmetry directly reduces to a collection of between one and four 5D SCFTs. Additionally, we find that in most cases, reduction of the tensor branch of a 6D SCFT yields a 5D generalization of a quiver gauge theory. These two reductions of the theory often correspond to different phases in the 5D theory which are in general connected by a sequence of flop transitions in the extended Kähler cone of the Calabi-Yau threefold. We also elaborate on the structure of the resulting conformal fixed points, and emergent flavor symmetries, as realized by M-theory on a canonical singularity.
Highlights
The moduli spaces of vacua are captured by deformations of the Calabi-Yau geometry, the anomaly polynomials are encoded in the intersection theory of the F-theory base [14,15,16], and the 6D omega-background partition function is captured by topological string amplitudes on the Calabi-Yau
Starting from 6D superconformal field theories (SCFTs) realized via F-theory, we show how reduction on a circle leads to a uniform perspective on the phase structure of the resulting 5D theories, and their possible conformal fixed points
Using the correspondence between F-theory reduced on a circle and M-theory on the corresponding elliptically fibered Calabi-Yau threefold, we show that each 6D SCFT with minimal supersymmetry directly reduces to a collection of between one and four 5D SCFTs
Summary
In this subsection we consider 5D SCFTs generated by a single collapsing divisor in a Calabi-Yau threefold. To decouple gravity in a local M-theory model, we either require S to contract to a point, or to a curve In the former case, we impose the stronger condition −KS > 0, which restricts us to the del Pezzo surfaces. A more unified perspective on all of these examples comes from first starting with the local geometry defined by a del Pezzo nine surface [41, 60] This can be viewed as P2 blown up at nine points, and is described by a Weierstrass model of the form: y2 = x3 + f4x + g6,. Flopping the zero section of this model, we blow down additional points to reach the various del Pezzo models These correspond in the field theory to adding mass deformations to the associated hypermultiplets. The condition we are finding is that this other surface must collapse to zero size
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