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
Distinguishing 6d (1,0) SCFTs: an extension to the geometric construction
We provide a new extension to the geometric construction of 6d (1, 0) SCFTs that encap- sulates Higgs branch structures with identical global symmetry but different spectra. In particular, we find that there exist distinct 6d (1, 0) SCFTs that may appear to share their tensor branch description, flavor symmetry algebras, and central charges. For example, such subtleties arise for the very even nilpotent Higgsing of (so4k,so4k) conformal matter; we pro- pose a method to predict at which conformal dimension the Higgs branch operators of the two theories differ via augmenting the tensor branch description with the Higgs branch chiral ring generators of the building block theories. Torus compactifications of these 6d (1, 0) SCFTs give rise to 4d N = 2 SCFTs of class S and the Higgs branch of such 4d theories are cap- tured via the Hall–Littlewood index. We confirm that the resulting 4d theories indeed differ in their spectra in the predicted conformal dimension from their Hall–Littlewood indices. We highlight how this ambiguity in the tensor branch description arises beyond the very even nilpotent Higgsing of (so4k,so4k) conformal matter, and hence should be understood for more general classes of 6d (1, 0) SCFTs.
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- Award ID(s):
- 1914679
- NSF-PAR ID:
- 10339046
- Date Published:
- Journal Name:
- ArXivorg
- ISSN:
- 2331-8422
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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. 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 1orII ) rather than elliptic curves (Kodaira typeI 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. However, in this case there are additional constraints on F‐theory constructions for coupling these theories to others. -
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