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

TL;DR

This paper explores the global symmetries of 6D SCFTs and LSTs with unpaired tensors in F-theory, revealing that these symmetries are subalgebras of 8 or 8 depending on the tensor's self-pairing, with new insights for theories involving nodal or cuspidal curves.

Contribution

It establishes the subalgebra structure of global symmetries for unpaired tensors in 6D theories, including cases with complex curve types, and identifies additional constraints for certain self-pairings.

Findings

Global symmetry algebra is a subalgebra of 8 for tensors with self-pairing -1.

For tensors with self-pairing -2, the symmetry is a subalgebra of 8, with extra F-theory constraints.

New results for theories involving nodal or cuspidal rational curves in F-theory constructions.

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.