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Motivated by its potential use in constraining the structure of 6D renormalization group flows, we determine the low energy dilaton-axion effective field theory of conformal and global symmetry breaking in 6D conformal field theories (CFTs). While our analysis is largely independent of supersymmetry, we also investigate the case of 6D superconformal field theories (SCFTs), where we use the effective action to present a streamlined proof of the 6D a -theorem for tensor branch flows, as well as to constrain properties of Higgs branch and mixed branch flows. An analysis of Higgs branch flows in some examples leads us to conjecture that in 6D SCFTs, an interacting dilaton effective theory may be possible even when certain four-dilaton four-derivative interaction terms vanish, because of large momentum modifications to four-point dilaton scattering amplitudes. This possibility is due to the fact that in all known D > 4 CFTs, the approach to a conformal fixed point involves effective strings which are becoming tensionless. [ABSTRACT FROM AUTHOR]

We explore higher-form symmetries of M- and F-theory compactified on elliptic fibrations, determined by the topology of their asymptotic boundaries. The underlying geometric structures are shown to be equivalent to known characterizations of the gauge group topology in F-theory via Mordell-Weil torsion and string junctions. We further study dimensional reductions of the 11d Chern-Simons term in the presence of torsional boundary G4-fluxes, which encode background gauge fields of center one-form symmetries in the lower-dimensional effective gauge theory. We find contributions that can be interpreted as 't Hooft anomalies involving the one-form symmetry which originate from a fractionalization of the instanton number of non-Abelian gauge theories in F-/M-theory compactifications to 8d/7d and 6d/5d. [ABSTRACT FROM AUTHOR]

Compactifications of the Chaudhuri-Hockney-Lykken (CHL) string to eight dimensions can be characterized by embeddings of root lattices into the rank 12 momentum lattice ΛM, the so-called Mikhailov lattice. Based on these data, we devise a method to determine the global gauge group structure including all U(1) factors. The key observation is that, while the physical states correspond to vectors in the momentum lattice, the gauge group topology is encoded in its dual. Interpreting a nontrivial π1(G) ≡ Z for the non-Abelian gauge group G as having gauged a Z 1-form symmetry, we also prove that all CHL gauge groups are free of a certain anomaly [1] that would obstruct this gauging. We verify this by explicitly computing Z for all 8D CHL vacua with rank (G) = 10. Since our method applies also to T² compactifications of heterotic strings, we further establish a map that determines any CHL gauge group topology from that of a "parent" heterotic model. [ABSTRACT FROM AUTHOR]

S -folds are a nonperturbative generalization of orientifold 3-planes which figure prominently in the construction of four-dimensional (4D) N = 3 superconformal field theories (SCFTs) and have also recently been used to realize examples of 4D N = 2 SCFTs. In this paper, we develop a general procedure for reading off the flavor symmetry experienced by D3-branes probing 7-branes in the presence of an S -fold. We develop an S -fold generalization of orientifold projection which applies to nonperturbative string junctions. This procedure leads to a different 4D flavor symmetry algebra depending on whether the S -fold supports discrete torsion. We also show that this same procedure allows us to read off admissible representations of the flavor symmetry in the associated 4D N = 2 SCFTs. Furthermore, this provides a prescription for how to define F-theory in the presence of S -folds with discrete torsion. [ABSTRACT FROM AUTHOR]

We present a general prescription for determining the global U(1) symmetries of six-dimensional superconformal field theories. We use the quiverlike gauge theory description of the tensor branch to identify candidate U(1) symmetries which can act on generalized matter. The condition that these candidate U(1)'s are free of Adler-Bell-Jackiw anomalies provides bottom-up constraints for U(1)'s. This agrees with the answer obtained from symmetry breaking patterns induced by Higgs branch flows. We provide numerous examples illustrating the details of this proposal. In the F-theory realization of these theories, some of these symmetries originate from deformations of non-Abelian flavor symmetries localized on a component of the discriminant, while others come from an additional generator of the Mordell-Weil group. We also provide evidence that some of these global U(1)'s do not arise from gauge symmetries, as would happen in taking a decoupling limit of a model coupled to six-dimensional supergravity. [ABSTRACT FROM AUTHOR]

Recent work on 6D superconformal field theories has established an intricate correspondence between certain Higgs branch deformations and nilpotent orbits of flavor symmetry algebras associated with T-branes. In this paper, we return to the stringy origin of these theories and show that many aspects of these deformations can be understood in terms of simple combinatorial data associated with multipronged strings stretched between stacks of intersecting 7-branes in F theory. These data let us determine the full structure of the nilpotent cone for each semisimple flavor symmetry algebra, and they further allow us to characterize symmetry-breaking patterns in quiverlike theories with classical gauge groups. An especially helpful feature of this analysis is that it extends to "short quivers" in which the breaking patterns from different flavor symmetry factors are correlated. [ABSTRACT FROM AUTHOR]