Membranes Wrapped on Holomorphic Curves

TL;DR

The paper develops gravity duals for twisted field theories arising from M-theory membranes wrapping holomorphic curves in Calabi–Yau n-folds by using a $U(1)^4$ truncation of $D=4$ $N=8$ gauged supergravity and uplifting to $D=11$. It derives and analyzes BPS equations for CY2–CY5, revealing UV $AdS_4$ regions and IR fixed points of type $AdS_2\times\Sigma$ or $AdS_2\times H^2$, including a flow across dimensions in CY4 and CY5 and connections to topological AdS black holes with scalar hair. The work also constructs generalized Kähler calibrations $oldsymbol{Omega}$, ensuring probe membranes can preserve supersymmetry in these backgrounds. Collectively, these results yield new AdS/CFT examples, clarify the IR-singularity structure, and illuminate the holographic interpretation of wrapped membranes in higher-dimensional Calabi–Yau geometries.

Abstract

We construct supergravity solutions dual to the twisted field theories arising when M-theory membranes wrap holomorphic curves in Calabi-Yau n-folds. The solutions are constructed in an Abelian truncation of maximal D=4 gauged supergravity and then uplifted to D=11. For four-folds and five-folds we find new smooth AdS/CFT examples and for all cases we analyse the nature of the singularities that arise. Our results provide an interpretation of certain charged topological AdS black holes. We also present the generalised calibration two-forms for the solutions.

Figures (6)

• Figure 1: Behaviour of the flows for an $S^2$ cycle in a Calabi--Yau two-fold
• Figure 2: Behaviour of the flows for an $H^2$ cycle in a Calabi--Yau two-fold
• Figure 3: Behaviour of the flows for an $S^2$ cycle in a Calabi--Yau three-fold
• Figure 4: Behaviour of the flows for an $H^2$ cycle in a Calabi--Yau three-fold
• Figure 5: Behaviour of the flows for an $S^2$ cycle in a Calabi--Yau four-fold