M-Fivebranes Wrapped on Supersymmetric Cycles

TL;DR

This work constructs gravity duals to twisted field theories arising from M5-branes wrapping general supersymmetric cycles, by employing maximal D=7 gauged supergravity and uplifting to D=11. It analyzes SLAG, Kähler, and exceptional cycles under Einstein or special curvature constraints, deriving BPS equations and identifying AdS_7-dimensions in the UV and IR fixed points of the wrapped theories, such as $AdS_4 imes H_3$, $AdS_3 imes H^4$, and $AdS_2 imes S^5$. The paper also computes central charges for the resulting two-dimensional CFTs, classifies the IR singularities as good or bad, and discusses the geometric and topological requirements on the calibrated cycles for supersymmetric solutions. These results provide new AdS/CFT examples and a unified framework for M5-branes wrapped on diverse supersymmetric cycles, offering directions for generalizations with richer gauge content and combined brane configurations.

Abstract

We construct supergravity solutions dual to the twisted field theories arising when M-theory fivebranes wrap general supersymmetric cycles. The solutions are constructed in maximal D=7 gauged supergravity and then uplifted to D=11. Our analysis covers Kahler, special Lagrangian and exceptional calibrated cycles. The metric on the cycles are Einstein, but do not necessarily have constant curvature. We find many new examples of AdS/CFT duality, corresponding to the IR superconformal fixed points of the twisted field theories.

Figures (6)

• Figure 1: Behaviour of the orbits for co-dimension two with $l=-1$. The $AdS_7$-type UV region is when $F$ and $x$ are both large. The singularity, IR(GS), in the IR region is of the good type.
• Figure 2: Behaviour of the orbits for co-dimension two with $l=1$. IR(GS) and IR(BS) indicate the good and bad singularities in the IR region, respectively.
• Figure 3: Behaviour of the orbits for co-dimension three with $l=-1$. Note the flow from the $AdS_7$-type region when $F,x$ are large to the IR fixed point and the flows to the good and bad singularities in the IR, IR(GS) and IR(BS), respectively.
• Figure 4: Behaviour of the orbits for co-dimension three with $l=1$.
• Figure 5: Behaviour of the orbits for co-dimension four with $l=-1$. Note the flow from the $AdS_7$-type region when $F,x$ are large to the IR fixed point and the flows to the good and bad singularities in the IR, IR(GS) and IR(BS), respectively.