Fivebranes Wrapped On Associative Three-Cycles

TL;DR

The paper constructs and analyzes supergravity solutions for M- and IIB-fivebranes wrapping associative 3-cycles in G2-holonomy manifolds, using a minimal ${ m D}=7$ gauged supergravity framework and uplifting to ${ m D}=10,11$. It demonstrates a flow from ${ m AdS}_7$-type regions to ${ m AdS}_4$ geometries in the M5 on hyperbolic 3-space case, implying a 3D SCFT in the IR for large $N$, and discusses wrapped IIB NS5-branes on ${ m S}^3$ where SUSY-breaking scenarios in 3D ${ m N}=1$ SYM might emerge. The analysis distinguishes between vanishing and non-vanishing topological mass, yielding explicit $h=0$ solutions with meron gauge fields and highlighting IR singularities for $h eq 0$, along with hyperbolic-space uplifts to ${ m AdS}_4$ and potential resolutions. Overall, the work extends AdS/CFT-type duals to twisted fivebrane theories on associative cycles, elucidating IR fixed points, operator deformations, and the role of topology and flux in moduli stabilization and SUSY breaking.

Abstract

We construct supergravity solutions corresponding to fivebranes wrapping associative three-cycles of constant curvature in manifolds of G_2-holonomy. The solutions preserve 2 supercharges and are first constructed in D=7 gauged supergravity and then lifted to D=10,11. We show that the low-energy theory of M-fivebranes wrapped on a compact hyperbolic three-space is dual to a superconformal field theory in D=3 by exhibiting a flow to an AdS_4 region. For IIB-fivebranes wrapped on a three-sphere we speculate on a connection with spontaneous supersymmetry breaking of pure N=1 super Yang-Mills theory in D=3.

Figures (3)

• Figure 1: Scalar potential of D=7 gauged supergravity with $h=1$.
• Figure 2: Behaviour of the orbits for the three-sphere when $h=1$. The $AdS_7$-type region is at $F\approx x^2$, for large $x$. The broken line is the separatrix. The singularity in the IR region is always of the bad type (BS).
• Figure 3: Behaviour of the orbits for hyperbolic spaces when $h=1$. The $AdS_7$-type region is at $F\approx x^2$, for large $x$, and flows to the IR fixed point or the good (GS) and bad (BS) singularities in the IR. The broken lines are the separatrices.