BPS M5-branes as Defects for the 3d-3d Correspondence

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.

arXiv comment26 pages, 16 figures

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• The gravity dual of supersymmetric gauge theories on a squashed three-sphere
• AdS spacetimes from wrapped M5 branes
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• Holography of 3d-3d correspondence at Large N
• Higher-Derivative Supergravity, Wrapped M5-branes, and Theories of Class $\mathcal{R}$
• Aspects of AdS${}_2$ classification in M-theory: Solutions with mesonic and baryonic charges
• A $\mathcal{N}=2$ Supersymmetric $Ad{S}_4$ Solution in M-theory with Purely Magnetic Flux
• Taming Supersymmetric Defects in 3d-3d Correspondence
• Kähler Uniformization from Holographic Renormalization Group Flows of M5-branes