Abstract
The authors study RG flows in six-dimensional (supersymmetric) CFTs, which allow only deformations through VEVs of tensor scalars and Higgs scalars, by constructing the effective field theories for the dilaton and axions. They discover a surprising absence of certain four-dilaton interactions that is completely counterintuitive to what is known in four or fewer dimensions and the authors connect it to the peculiar large-momentum behavior of four-point functions, which they explain with the occurrence of effective strings in CFTs above four dimensions.
Highlights
One of the important features of quantum field theories is that they can be organized according to a hierarchy of scales which can be related by renormalization group (RG) flows
Conformal field theories (CFTs) are of particular significance since they arise from fixed points of the renormalization group, and the general structure of these theories indicates that there is a sense in which information is lost in passing from the ultraviolet (UV) to the infrared (IR)
Motivated by the prospect of determining possible constraints on the structure of 6D RG flows, our aim in this paper will be to construct the dilaton-axion effective action associated with spontaneous breaking of conformal symmetry, when it is accompanied by the breaking of a global continuous symmetry
Summary
One of the important features of quantum field theories is that they can be organized according to a hierarchy of scales which can be related by renormalization group (RG) flows. Motivated by the prospect of determining possible constraints on the structure of 6D RG flows, our aim in this paper will be to construct the dilaton-axion effective action associated with spontaneous breaking of conformal symmetry, when it is accompanied by the breaking of a global continuous symmetry This sort of situation is rather generic in 6D SCFTs, and arises whenever. Many 6D SCFTs have a deformation to a tensor branch in which the theory on the tensor branch has a Higgs branch In this case, we can explicitly track in the resulting low-energy gauge theory how various contributions to the dilaton-axion effective action are generated. At the level of explicit Feynman diagrams we find no way to generate a purely Higgs branch contribution to this interaction term This is a rather surprising result, and it leads us to conjecture that for Higgs branch flows of 6D SCFTs, the term φ2□2φ2 vanishes. Some additional aspects of the dilaton-axion effective action are included in Appendix
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