Tinkertoys for the twisted D-series

Abstract

Abstract:We study 4D N = 2 superconformal field theories that arise from the compactification of 6D N = (2, 0) theories of type D N on a Riemann surface, in the presence of punctures twisted by a Z 2 outer automorphism. Unlike the untwisted case, the family of SCFTs is in general parametrized, not by M g,n , but by a branched cover thereof. The classification of these SCFTs is carried out explicitly in the case of the D 4 theory, in terms of three-punctured spheres and cylinders, and we provide tables of properties of twisted punctures for the D 5 and D 6 theories. We find realizations of Spin (8) and Spin(7) gauge theories with matter in all combinations of vector and spinor representations with vanishing β-function, as well as Sp(3) gauge theories with matter in the 3-index traceless antisymmetric representation.

Compactifications of 5d SCFTs with a twist

“…In this case we can gauge an SU(2) ⊂ USp (4) SCFT by an SU(2) gauge group, while figure 7 (c) describes an SU(3) + 1S + 1F gauge theory. This suggests that these are dual as was discovered in [29,31].…”

“…In the Z 3 case we first examine various low N cases identifying these with various known 4d SCFTs. Interestingly one of these is the recently discovered rank 1 SU(4) SCFT found in [20]. Besides providing an additional string theory construction for this theory, by examining its mass deformation, we get string theory constructions also for other rank 1 SCFT generated by mass deforming the SU(4) SCFT, originally introduced in [21].…”

“…We find one describes a weak SU(2) gauging of the aforementioned SCFT (see figure 11 (b)) while the other describing a weak SO(k + 2) + kV gauge theory (see figure 11 (c)). There is indeed a known duality of this form [34], leading us to identify the SU(2) × USp(2k) SCFT appearing in these dualities with the one resulting from the twisted compactification.…”

“…In the k even case, this theory can be constructed by the compactification of a D type 6d (2, 0) theory with twist [34] which allows determining its properties. We can perform some consistency checks on this identification.…”

“…In addition we add a Z 2 twist in the outer automorphism of D k+1 on one of the cycles of the torus. We then get both theories in the bottom of figure 13 as different pair of pants decompositions of this Riemann surface (see also [31] for an example of this type of dualities for the twisted A (2, 0) theory).…”