E‐String Theory on Riemann Surfaces

Abstract

We study compactifications of the 6d E-string theory, the theory of a small E 8 instanton, to four dimensions. In particular we identify N = 1 field theories in four dimensions corresponding to compactifications on arbitrary Riemann surfaces with punctures and with arbitrary non-abelian flat connections as well as fluxes for the abelian sub-groups of the E 8 flavor symmetry. This sheds light on emergent symmetries in a number of 4d N = 1 SCFTs (including the 'E7 surprise' theory) as well as leads to new predictions for a large number of 4-dimensional exceptional dualities and symmetries.

D-type conformal matter and SU/USp quivers

“…This is one way in which one can see that the (D N +3 , D N +3 ) minimal conformal matter can be thought of as a generalization of the rank one E-string, which from the field theory viewpoint is done by the addition of vectors and hypermultiplets. We also note that the naive expected symmetry SO (16) in the E-string case is enhanced to E 8 . We shall later discuss the mechanism leading to this enhancement from the gauge theory viewpoint.…”

“…In particular, there is an alternative way to think of the minimal (D N +3 , D N +3 ) conformal matter in such a way that is naturally generalizable to the non-minimal as well as more general cases. This is part of a much larger story that will be considered in a different publication [17], but when applied to the case of the minimal (D N +3 , D N +3 ) conformal matter, it leads to other 4d field theories that should lead to dual descriptions of the same 4d SCFT. We discuss this aspect in appendix B.…”

“…Regarding that last part, we note that, with our normalization of flux, in some cases the value of the flux will be fractional and in those cases one also has flux turned on in the center of the group, see appendix C of [16] for a discussion on this type of effects.…”

“…In this section we study these 5d gauge theories when various fluxes are turned on under the compactifications. The 6d fluxes naturally reduce to domain wall configurations in the 5d gauge theories [16]. We will call this type of domain walls as 'flux domain walls'.…”

AdS7/CFT6 with orientifolds

“…3 (It is true however that such embeddings have been very fruitful. For instance, they allow us to classify six-dimensional theories [29] and, partially, their compactifications [39][40][41][42][43][44]; compute quantities such as dimensions of moduli spaces [32], defect and autmorphism groups [45,46]; determine RG flows and their hierarchy [47,48] and the global symmetries [28,49,50]; compute anomalies from the six-dimensional anomaly polynomial [51]. )…”