2024/11/05 by Simone Giacomelli, William Harding, Giacomelli, Simone +5
Mathematics · #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2411.03425
openalex publication_date 2024/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
A surprising relation between 4d N=2 class S superconformal field theories of Type-A and 6d N=(1,0) orbi-instanton theories is investigated. We find that all of the theories in the former class can be obtained by a series of deformations of the 4d theories arising from compactifying the latter on a torus. This is demonstrated by examining Fayet--Iliopoulos (FI) deformations of the E8-shaped magnetic quivers of the orbi-instanton theories whose body fits into the affine E8 Dynkin diagram with a tail attached. Turning on FI parameters at the appropriate gauge groups leads, in stages, to E7-shaped, E6-shaped, and general star-shaped quivers, where the latter are magnetic quivers for the class S theory of Type-A on a sphere with punctures. Deforming a suitable star-shaped quiver, one obtains a magnetic quiver of the Type-A class S theory with general genus and an arbitrary number of punctures. Given such a theory, we also propose the inverse algorithm, thereby determining a parent orbi-instanton theory. This is achieved by uplifting the corresponding magnetic quiver step by step to the star-shaped, E6-shaped, E7-shaped, and E8-shaped quivers, where at each step all of the underbalanced nodes, possessing non-zero FI parameters, are dualized. The latter E8-shaped quiver then characterizes the 6d orbi-instanton theory from which the class S theory in question originates.