Two 6D origins of 4D SCFTs: Class <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">S</mml:mi></mml:math> and 6D (1, 0) on a torus
Florent Baume, Monica Jinwoo Kang, Craig Lawrie
Abstract
We consider all 4D $\mathcal{N}=2$ theories of class $\mathcal{S}$ arising from the compactification of exceptional 6D (2, 0) SCFTs on a three-punctured sphere with a simple puncture. We find that each of these 4D theories has another origin as a 6D (1, 0) SCFT compactified on a torus, which we check by identifying and comparing the central charges and the flavor symmetry. Each 6D theory is identified with a complex structure deformation of $({\mathfrak{e}}_{n},{\mathfrak{e}}_{n})$ minimal conformal matter, which corresponds to a Higgs branch renormalization group flow. We find that this structure is precisely replicated by the partial closure of the punctures in the class $\mathcal{S}$ construction. We explain how the plurality of origins makes manifest some aspects of 4D SCFTs, including flavor symmetry enhancements and determining if it is a product SCFT. We further highlight the string theoretic basis for this identification of 4D theories from different origins via mirror symmetry.