Exact Half-BPS Flux Solutions in M-theory I, Local Solutions

Abstract

The complete eleven-dimensional supergravity solutions with 16 supersymmetries on manifolds of the form $Ad{S}_3\times S^3\times S^3\times \Sigma$, with isometry $SO(2,2)\times SO(4)\times SO(4)$, and with either $Ad{S}_4\times S^7$ or $Ad{S}_7\times S^4$ boundary behavior, are obtained in exact form. The two-dimensional parameter space $\Sigma$ is a Riemann surface with boundary, over which the product space $Ad{S}_3\times S^3\times S^3$ is warped. By mapping the reduced BPS equations to an integrable system of the sine-Gordon/Liouville type, and then mapping this integrable system onto a linear equation, the general local solutions are constructed explicitly in terms of one harmonic function on $\Sigma$, and an integral transform of two further harmonic functions on $\Sigma$. The solutions to the BPS equations are shown to automatically solve the Bianchi identities and field equations for the 4-form field, as well as Einstein's equations. The solutions we obtain have non-vanishing 4-form field strength on each of the three factors of $Ad{S}_3\times S^3\times S^3$, and include fully back-reacted M2-branes in $Ad{S}_7\times S^4$ and M5-branes in $Ad{S}_4\times S^7$. No interpolating solutions exist with mixed $Ad{S}_4\times S^7$ and $Ad{S}_7\times S^4$ boundary behavior. Global regularity of these local solutions, as well as the existence of further solutions with neither $Ad{S}_4\times S^7$ nor $Ad{S}_7\times S^4$ boundary behavior will be studied elsewhere.

62 pages, 2 figures, references and clarifications on supergroups added

Cited by in corpus (71)

• Warped $Ad{S}_6\times S^2$ in Type IIB supergravity II: Global solutions and five-brane webs
• Supersymmetric Janus Solutions in Four Dimensions
• Near-horizon solutions for D3-branes ending on 5-branes
• Two dimensional $\mathcal{N}=(0,4)$ quivers dual to AdS${}_3$ solutions in massive IIA
• Half-BPS Solutions locally asymptotic to AdS_3 x S^3 and interface conformal field theories
• Janus solutions in M-theory
• 1/4 BPS AdS${}_3$/CFT${}_2$
• Superconformal surfaces in four dimensions
• M-theory Solutions Invariant under $D(2,1;\gamma )\oplus D(2,1;\gamma )$
• Janus solutions in six-dimensional gauged supergravity
• Scaling limit of N=6 superconformal Chern-Simons theories and Lorentzian Bagger-Lambert theories
• Holographic duals of Boundary CFTs
• Type II Solutions on AdS${}_3\times S^3\times S^3$ with Large Superconformal Symmetry
• Exact half-BPS string-junction solutions in six-dimensional supergravity
• $\mathcal{N}=(2,2)$ AdS${}_3$ from D3-branes wrapped on Riemann surfaces
• Boundary entropy of supersymmetric Janus solutions
• Holographic RG-flows and Boundary CFTs
• Electrostatic Description of Five-dimensional SCFTs
• Phases of Holographic Interfaces
• Supersymmetric AdS3 X S2 M-theory geometries with fluxes
• Searching for surface defect CFTs within AdS${}_3$
• ${\text{AdS}}_2\times {\text{S}}^2\times {\text{CY}}_2$ solutions in Type IIB with 8 supersymmetries
• M5-branes and Wilson Surfaces in AdS${}_7$/CFT${}_6$ Correspondence
• All $\mathcal{N}=(8,0)$ AdS${}_3$ solutions in 10 and 11 dimensions
• Exact Half-BPS Flux Solutions in M-theory III: Existence and rigidity of global solutions asymptotic to AdS4 x S7
• Wilson Surface Central Charge from Holographic Entanglement Entropy
• AdS${}_3$ solutions with $\mathcal{N}=(3,0)$ from S${}^3\times$S${}^3$ fibrations
• Open Worldsheets for Holographic Interfaces
• Janus Black Holes
• Exact Half-BPS Flux Solutions in M-theory with $D(2,1;c^{\prime };0{)}^2$ Symmetry: Local Solutions
• Surface defects in holographic 5d SCFTs
• Holographic description of SCFT${}_5$ compactifications
• N=(0,4) Black String Chains
• Entanglement entropy of Wilson surfaces from bubbling geometries in M-theory
• Aspects of AdS${}_2$ classification in M-theory: Solutions with mesonic and baryonic charges
• Supersymmetric Janus solutions of dyonic $ISO(7)$-gauged $\mathcal{N}=8$ supergravity
• $\mathcal{N}=(8,0)$ AdS vacua of three-dimensional supergravity
• A note on co-dimension 2 defects in N=4,d=7 gauged supergravity
• Consistent truncations of supergravity and $\frac{1}{2}$-BPS RG flows in $4d$ SCFTs
• String Junctions and Holographic Interfaces
• Warped $Ad{S}_2$ and $SU(1,1|4)$ symmetry in Type IIB
• Multi-faced Black Janus and Entanglement
• Spin 2 fluctuations in 1/4 BPS AdS${}_3$/CFT${}_2$
• $\mathcal{N}=(1,1)$ supersymmetric AdS${}_3$ in 10 dimensions
• Holography for 2d $\mathcal{N}=(0,4)$ quantum field theory
• Local gravitational solutions dual to M2-branes intersecting and/or ending on M5-branes
• On Type IIA AdS${}_3$ solutions and massive GK geometries
• Double Trace Interfaces
• Relating Conifold Geometries to NS5-branes
• Holographic Surface Defects in $D=5$, $N=4$ Gauged Supergravity
• Observations on BPS observables in 6d
• Conformal Defect Solutions in $N=2,D=4$ Gauged Supergravity
• Janus solutions in three-dimensional N=8 gauged supergravity
• Wilson loops for 5d and 3d conformal linear quivers
• AdS${}_3\times$ S${}^2$ in IIB with small $\mathcal{N}=(4,0)$ supersymmetry
• Entanglement entropy of Wilson loops: Holography and matrix models
• Holographic entanglement entropy of surface defects
• Holographic Entropy and Calabi's Diastasis
• Lifshitz-like Janus Solutions
• Spin-$2$ operators in AdS${}_2$/CFT${}_1$
• $N=(2,0)$ AdS${}_3$ Solutions of M-theory
• Beyond LLM in M-theory
• A supersymmetric holographic dual of a fractional topological insulator
• Exact M-Theory Solutions, Integrable Systems, and Superalgebras
• Rigidity of SU(2,2|2)-symmetric solutions in Type IIB
• BPS surface operators and calibrations
• The conformal brane-scan: an update
• From Large to Small $\mathcal{N}=(4,4)$ Superconformal Surface Defects in Holographic 6d SCFTs
• Exact solutions to complex Type IIB supergravity for complex superalgebra $F(4)$ and its real forms
• $SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs
• Near Horizon Geometry of Strings Ending on Intersecting D8/D4-branes