M-theory Solutions Invariant under $D(2,1;\gamma )\oplus D(2,1;\gamma )$

Abstract

We simplify and extend the construction of half-BPS solutions to 11-dimensional supergravity, with isometry superalgebra D(2,1;γ) \oplus D(2,1;γ). Their space-time has the form AdS_3 x S^3 x S^3 warped over a Riemann surface Σ. It describes near-horizon geometries of M2 branes ending on, or intersecting with, M5 branes along a common string. The general solution to the BPS equations is specified by a reduced set of data (γ, h, G), where γis the real parameter of the isometry superalgebra, and h and G are functions on Σwhose differential equations and regularity conditions depend only on the sign of γ. The magnitude of γenters only through the map of h, G onto the supergravity fields, thereby promoting all solutions into families parametrized by |γ|. By analyzing the regularity conditions for the supergravity fields, we prove two general theorems: (i) that the only solution with a 2-dimensional CFT dual is AdS_3 x S^3 x S^3 x R^2, modulo discrete identifications of the flat R^2, and (ii) that solutions with γ< 0 cannot have more than one asymptotic higher-dimensional AdS region. We classify the allowed singularities of h and G near the boundary of Σ, and identify four local solutions: asymptotic AdS_4/Z_2 or AdS_7' regions; highly-curved M5-branes; and a coordinate singularity called the "cap". By putting these "Lego" pieces together we recover all known global regular solutions with the above symmetry, including the self-dual strings on M5 for $\gamma <0$, and the Janus solution for γ> 0, but now promoted to families parametrized by |γ|. We also construct exactly new regular solutions which are asymptotic to AdS_4/Z_2 for γ< 0, and conjecture that they are a different superconformal limit of the self-dual string.

61 pages, 6 figures, references and acknowledgments added in version 2

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• $\mathcal{N}=(2,2)$ AdS${}_3$ from D3-branes wrapped on Riemann surfaces
• Broken global symmetries and defect conformal manifolds
• Phases of Holographic Interfaces
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• Wilson Surface Central Charge from Holographic Entanglement Entropy
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• $\mathcal{N}=2$ Supersymmetric Janus Solutions and Flows: From Gauged Supergravity to M Theory
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• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
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• Topological M-Strings and Supergroup WZW Models
• $\mathcal{N}=(1,1)$ supersymmetric AdS${}_3$ in 10 dimensions
• Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
• On Type IIA AdS${}_3$ solutions and massive GK geometries
• Janus and Hades in M-theory
• Janus and RG interfaces in three-dimensional gauged supergravity II: General $\alpha$
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• A Lagrangian for self-dual strings
• The conformal brane-scan: an update
• Comparing top-down and bottom-up holographic defects and boundaries
• Complex D($2,1;\zeta$) and spin chain solutions from Chern-Simons theory
• Holographic BCFT Spectra from Brane Mergers
• From Large to Small $\mathcal{N}=(4,4)$ Superconformal Surface Defects in Holographic 6d SCFTs
• $SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs
• Near Horizon Geometry of Strings Ending on Intersecting D8/D4-branes