Pairing 6D SCFTs
Abstract
In this note, we discuss families of orbifolds underlying 6D SCFT Ftheory models and find a novel pairing structure in the SCFT landscape. Inspection of the rational functions defining models with a common Ftheory endpoint leads us to naturally to pair them and find compatible extended groupings matching endpoint collections recently characterized in correspondence with homomorphisms of the ADE subgroups of $SU(2)$ into $E_8.$ We confirm this proposed pairing closely links the proposed SCFT family pairs via explicit computation of gauge algebras. We find these typically pair precisely by a fixed additional gauge summand. The underlying $\mathbb{C}^2$ orbifold pairing is distinct from the lattice/overlattice orbifold duality which lacks closure on the set of SCFT endpoints. The previously established partial order on endpoints is respected by this pairing as is the distinguished role of certain theories allowing M5brane fraction reassembly which appear here as selfdual endpoints. This duality manifests in the known tower structure of endpoints to a mirror in a tower below which we show exists naturally as an infinite chain of endpoints extrapolated to negative valuations of the rational functions defining endpoints. We also detail a related simple combinatorial prescription for all rational functions defining endpoint families.
 Publication:

arXiv eprints
 Pub Date:
 February 2019
 arXiv:
 arXiv:1903.00079
 Bibcode:
 2019arXiv190300079M
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 27 pages