Classifying global symmetries of 6D SCFTs

Abstract

We characterize the global symmetries for the conjecturally complete collection of all six dimensional superconformal field theories (6D SCFTs) which are realizable in F-theory and have no frozen singularities. We provide comprehensive checks of earlier 6D SCFT classification results via an alternative geometric approach yielding new restrictions which eliminate certain theories. We achieve this by directly constraining elliptically fibered Calabi-Yau (CY) threefold Weierstrass models and find this allows bypassing all anomaly cancellation machinery. This approach reduces the problem of classifying which 6D SCFT gauge and global symmetries are realizable in F-theory models before RG-flow to characterizing features of elliptic fibrations associated to these theories obtained by analysis of polynomials determining their local models. We supply an algorithm with implementation producing from a given SCFT base an explicit listing of all compatible gauge enhancements and their associated global symmetry maxima consistent with the geometric constraints we derive while making manifest the corresponding geometric ingredients for these symmetries including any possible Kodaira type realizations of each algebra summand. In mathematical terms, this amounts to determining all potentially viable non-compact CY threefold elliptic fibrations at finite distance in the moduli space with Weil-Petersson metric which meet certain requirements including the transverse pairwise intersection of singular locus components. We provide local analysis exhausting nearly all CY consistent transverse singular fiber collisions, global analysis concerning all viable gluings of these local models into larger configurations, and many novel constraints on singular locus component pair intersections and global fiber arrangements. We also investigate which transitions between 6D SCFTs can result from gauging of global symmetries and find that continuous degrees of freedom can be lost during such transitions.

Revisiting the classifications of 6d SCFTs and LSTs

“…Our conjecture stems from the fact that this combined classification exhausts all the possible tensor branches that can be obtained by putting together gauge theories with known nongauge theories like the E-string theory and A 1 (2, 0) theory. We caution that there is a small set of theories whose F-theory construction was proposed in [1,3] but a closer look in [12] (see also [13,14]) revealed an inconsistency in the proposed constructions of those theories. It would be worthwhile to investigate whether such theories can be given a consistent construction in the frozen phase of F-theory.…”

Fibers add flavor. Part I. Classification of 5d SCFTs, flavor symmetries and BPS states

“…where (u, v) are local coordinates on the base B. The non-minimal singularity at u = 0 = v will correspond to collisions of two non-compact curves in the base, u = 0 and v = 0, above which the fiber has standard minimal Kodaira singularities, associated to some Lie algebras g ν , ν = u, v. F-theory compactified on Y gives a 6d SCFT, with flavor symmetry g (6d) F [45,63,64], and it is this flavor symmetry, and the remnants of this symmetry that percolate down to 5d, which we will encode in our characterization of the resolution geometries, and in their graphical presentation in terms of CFDs.…”

Global Tensor‐Matter Transitions in F‐Theory

“…For the resolution of a single SCP, the modifications in the reducible anomaly coefficients in the non-Abelian sector given by (61) and (62) …”

“…The blow-up procedure has been summarized in Figure 10. Such a theory is known as (E 7 , SO(7)) minimal conformal matter describing a half-M5 brane on top of the E 7 singularity [5,[59][60][61]. One might speculate whether the top encodes some non-trivial information of the above theory.…”