F-theory and Unpaired Tensors in 6D SCFTs and LSTs

TL;DR

The paper advances the field-theoretic understanding of 6D SCFTs and LSTs with a single unpaired tensor by leveraging F-theory constraints. It demonstrates that a -1 self-pairing enforces global symmetries as subalgebras of $\mathfrak{e}_8$, extending known results to Kodaira types I1 and II, and shows that -2 self-pairing yields subalgebras of $\mathfrak{su}(2)$ with additional coupling constraints. Through detailed analysis of residual vanishings, fiber types, and tangencies, the work derives explicit maximal adjacencies for various Kodaira fibers and clarifies how tangencies modify gauging conditions. It also identifies unusual configurations not realizable in F-theory, underscoring gaps between geometric constraints and purely field-theoretic expectations and motivating further development toward a complete 6D SCFT/LST classification. Overall, the results substantially constrain possible couplings in multi-tensor systems and refine the role of global symmetry as a guiding principle in 6D theories.

Abstract

We investigate global symmetries for 6D SCFTs and LSTs having a single "unpaired" tensor, that is, a tensor with no associated gauge symmetry. We verify that for every such theory built from F-theory whose tensor has Dirac self-pairing equal to -1, the global symmetry algebra is a subalgebra of $\mathfrak{e}_8$. This result is new if the F-theory presentation of the theory involves a one-parameter family of nodal or cuspidal rational curves (i.e., Kodaira types $I_1$ or $II$) rather than elliptic curves (Kodaira type $I_0$). For such theories, this condition on the global symmetry algebra appears to fully capture the constraints on coupling these theories to others in the context of multi-tensor theories. We also study the analogous problem for theories whose tensor has Dirac self-pairing equal to -2 and find that the global symmetry algebra is a subalgebra of $\mathfrak{su}(2)$. However, in this case there are additional constraints on F-theory constructions for coupling these theories to others.