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

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.

21 pages

References in corpus (5)

• 6d Conformal Matter
• Holography for (1,0) theories in six dimensions
• Anomaly polynomial of E-string theories
• 6d, N=(1,0) Coulomb Branch Anomaly Matching
• Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds

Cited by in corpus (15)

• Universal Features of BPS Strings in Six-dimensional SCFTs
• On Exceptional Instanton Strings
• Revisiting the classifications of 6d SCFTs and LSTs
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• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• T-Branes, String Junctions, and 6D SCFTs
• Dual Little Strings from F-Theory and Flop Transitions
• Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
• Classifying Global Symmetries of 6D SCFTs
• Bootstrapping (D, D) Conformal Matter
• Flavor Symmetries and Automatic Enhancement in the 6d Supergravity Swampland
• Non-Geometric Vacua of the $\text{Spin}(32)/{\mathbb{Z}}_2$ Heterotic String and Little String Theories
• Isomorphisms of 4d N=2 SCFTs from 6d