F‐theory and unpaired tensors in 6D SCFTs and LSTs

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 . 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 I₁ or II) rather than elliptic curves (Kodaira type I₀). 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 . However, in this case there are additional constraints on F‐theory constructions for coupling these theories to others.