Abstract
We study supersymmetric probe M5-branes in the AdS_4 solution that arises from M5-branes wrapped on a hyperbolic 3-manifold M_3. This amounts to introducing internal defects within the framework of the 3d-3d correspondence. The BPS condition for a probe M5-brane extending along all of AdS_4 requires it to wrap a surface embedded in an S^2-fibration over M_3. We find that the projection of this surface to M_3 can be either a geodesic or a tubular surface around a geodesic. These configurations preserve an extra U(1) symmetry, in addition to the one corresponding to the R-symmetry of the dual 3d N=2 gauge theory. BPS M2-branes can stretch between M5-branes wrapping geodesics. We interpret the addition of probe M5-branes on a closed geodesic in terms of conformal Dehn surgery.
Highlights
Gives rise in the IR to an AdS4 solution of 11d supergravity
We study supersymmetric probe M5-branes in the AdS4 solution that arises from M5-branes wrapped on a hyperbolic 3-manifold M3
In the AdS4 geometries that we study, what remains of the UV cotangent bundle T ∗M3 is the unit cotangent bundle T1∗M3 described by the metric gin (3.15) — the radial direction in the cotangent fibers has been absorbed in the radial direction of AdS4 and in ρ
Summary
We start by reviewing the AdS4 solution of M-theory that we will be considering in this paper. It is of the form AdS4 × Y7, where Y7 is an S4-fibration over a hyperbolic 3-manifold M3 This solution was shown in [14] to arise as a special case of a general class of N = 2 supersymmetric AdS4 geometries describing the near-horizon limit of M5-branes wrapping a special Lagrangian 3-cycle in a Calabi-Yau 3-fold (the generality of this class was proven in [15]). The metric for this class of solutions takes the form ds211.
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