Abstract
We study 6d superconformal field theories (SCFTs) compactified on a circle with arbitrary twists. The theories obtained after compactification, often referred to as 5d Kaluza-Klein (KK) theories, can be viewed as starting points for RG flows to 5d SCFTs. According to a conjecture, all 5d SCFTs can be obtained in this fashion. We compute the Coulomb branch prepotential for all 5d KK theories obtainable in this manner and associate to these theories a smooth local genus one fibered Calabi-Yau threefold in which is encoded information about all possible RG flows to 5d SCFTs. These Calabi-Yau threefolds provide hitherto unknown M-theory duals of F-theory configurations compactified on a circle with twists. For certain exceptional KK theories that do not admit a standard geometric description we propose an algebraic description that appears to retain the properties of the local Calabi-Yau threefolds necessary to determine RG flows to 5d SCFTs, along with other relevant physical data.
Highlights
There has been a resurgence of interest in the problem of classifying 5d superconformal field theories (SCFTs), with a particular emphasis on exploring the relationship between 5d UV fixed points and 6d UV fixed points [1,2,3,4,5,6,7,8,9,10,11]
The motivation for studying this relationship is the observation that all known 5d SCFTs can be organized into families of theories whose “progenitors” are 6d SCFTs compactified on a circle [1, 2], and every 6d SCFT compactified on a circle provides a natural starting point for the systematic identification of a large family of 5d SCFTs
All known examples of such theories are characterized by the emergence of an intrinsic length scale that is interpreted as the size of a compactification circle, and it has been argued that each of these theories is a circle compactification of a 6d SCFT possibly twisted by the action of a discrete global symmetry;1 see for example [2,3,4, 18, 24,25,26,27,28]
Summary
There has been a resurgence of interest in the problem of classifying 5d superconformal field theories (SCFTs), with a particular emphasis on exploring the relationship between 5d UV fixed points and 6d UV fixed points [1,2,3,4,5,6,7,8,9,10,11]. The different twists of a 6d SCFT T are characterized by equivalence classes in the group of discrete global symmetries of T We show that these equivalence classes can be described by foldings of the graphs ΣT associated to T along with choice of an outer automorphism for each gauge algebra appearing in the low energy theory on the tensor branch of T. This is done by compactifying the low energy gauge theory appearing on the tensor branch of the corresponding 6d SCFT on a circle with the corresponding twist. The notebook converts the prepotential into triple intersection numbers for the associated geometry and displays these intersection numbers in a graphical form
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