A $\mathcal{N}=2$ Supersymmetric $AdS_4$ Solution in M-theory with Purely Magnetic Flux

TL;DR

This paper constructs a new $\mathcal{N}=2$ supersymmetric $AdS_4$ solution in M-theory with purely magnetic flux by applying non-Abelian T-duality to the $AdS_4\times CP^3$ background of ABJM, followed by an Abelian T-duality and uplift to eleven dimensions. The resulting geometry fits within the Gauntlett–Gabella purely magnetic class and features a 7d internal $SU(2)$ structure, with KK-monopoles and wrapped M5-branes shaping the dual CFT data. Surprisingly, the holographic free energy scales as $\mathcal{F}\sim N^{3/2}$, even though the natural M5-brane interpretation would suggest $N^3$ behavior, indicating that KK-monopoles (not wrapped M5-branes) play the dominant color role in the fundamental region. The work thereby extends the space of explicit $AdS_4$ solutions with $\mathcal{N}=2$ in M-theory and raises interesting questions about the precise CFT duals in the presence of non-compact NAT directions and purely magnetic flux.

Abstract

We find a new $\mathcal{N}=2$ $AdS_4$ solution in M-theory supported by purely magnetic flux via a sequence of abelian and non-abelian T-dualities. This provides the second known example in this class besides the uplift of the Pernici and Sezgin solution to 7d gauged supergravity constructed in the eighties. We compute the free energy of the solution, and show that it scales as $N^{3/2}$. It is intriguing that even though the natural holographic interpretation is in terms of M5-branes wrapped on a special Lagrangian 3-cycle, this solution does not exhibit the expected $N^3$ behavior.