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Physical origin of non‑abelian enhancement to USp(2)

Ascertain a physical mechanism that explains why the cohomological grading, interpreted as U(1)_r weights in four‑dimensional N=2 SCFTs, admits a non‑abelian enhancement to a USp(2) outer automorphism acting on the relative semi‑infinite cohomology H^{∞/2+•}(g_{-2h∨}, g, V_matter) and on the underlying differential graded vertex algebra C(g_{-2h∨}, g, V_matter).

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Background

The authors prove an unexpected USp(2) outer automorphism acting on cohomology and the underlying complex, extending the natural U(1) grading associated with U(1)_r. This non‑abelian enhancement lacks a clear physical explanation in four dimensions.

They suggest possible three‑dimensional origins (e.g., SU(2)_C enhancement) but emphasize that a definitive four‑dimensional rationale is unknown.

References

The appearance of an ${\rm USp}(2)$ outer automorphism on relative semi-infinite cohomology is quite surprising from the perspective of four-dimensional physics. The cohomological grading is interpreted physically as weights of the ${\rm U}(1)_r$ $R$-symmetry of the physical theory and we do not know of a physical reason why this should have a non-abelian enhancement, though upon reduction to three dimensions it seems plausible that the enhancement could be related to the ${\rm SU}(2)_C$ enhancement of ${\rm U}(1)_r$ (cf. footnote \ref{footnote:outer_speculations}).

— On the semi-infinite cohomology of graded-unitary vertex algebras (2509.10364 - Beem et al., 12 Sep 2025) in Section 4.2 (Outer automorphisms from the Q^-Q^+ lemma)