A note on dualities of F(4) type 3d N = 5 SCFTs

TL;DR

The paper investigates the landscape of 3d $N=5$ SCFTs by proposing a nonperturbative duality between an exceptional $F(4)$-based SCFT and an ABJ-type theory, and then tests this proposal with a detailed superconformal index comparison. The authors identify a concrete dual pair, Spin(7)$_{-3}\times SU(2)_2$/\mathbb{Z}_2 and Spin(4)$_{-2}\times USp(2)_1$, and further generate a triality by gauging a 1-form symmetry to obtain $SO(4)_{-2}\times USp(2)_1$ and a unitary dual $[U(3)_4\times U(1)_4]/\mathbb{Z}_2$. They compute the 3d superconformal index for these theories (up to order $x^4$) in the Kapustin convention and find exact matches between the dual descriptions, providing nonperturbative evidence for the proposed dualities. This work advances the classification of $N=5$ SCFTs and demonstrates how index matching can reveal otherwise inaccessible IR equivalences, with potential extensions to other exceptional algebras. The results also illustrate how dualities can simplify partition-function computations by moving to more tractable dual descriptions.

Abstract

We suggest a new duality between a pair of 3d N = 5 SCFTs, one of ABJ type and one based on the exceptional superalgebra F (4). Our main evidence for the proposed duality is the matching of the superconformal index. In addition to the intrinsic interest in dualities between strongly coupled field theories, the result can also be useful in the classification of 3d N = 5 SCFTs.