Physical interpretation of symplectic outer automorphism groups

Ascertain a physical interpretation of the symplectic outer automorphism groups acting by vertex algebra automorphisms on the differential graded vertex algebras C(g_{-2h∨}, g, V_matter) underlying relative semi-infinite cohomology of weak graded‑unitary vertex algebras and on their cohomology H^{∞/2+•}(g_{-2h∨}, g, V_matter), including clarifying whether these automorphisms reflect known physical structures or dualities.

Background

The paper proves that the relative semi-infinite cohomology of weak graded-unitary vertex algebras carries a unitary action of USp(2), analogous to Lefschetz symmetry in Kähler geometry. This symmetry arises from the symplectic fermion sector used in the BRST construction and extends a natural U(1) grading.

While the mathematical existence of these outer automorphisms is established, their physical meaning in four-dimensional N=2 SCFTs is not explained. The authors point out potential links (e.g., to S-duality or SU(2)_C in three dimensions), but emphasize that the interpretation remains open.