Exact Half-BPS Flux Solutions in M-theory III: Existence and rigidity of global solutions asymptotic to AdS4 x S7

Abstract

The BPS equations in M-theory for solutions with 16 residual supersymmetries, $SO(2,2)\times SO(4)\times SO(4)$ symmetry, and $Ad{S}_4\times S^7$ asymptotics, were reduced in [arXiv:0806.0605] to a linear first order partial differential equation on a Riemann surface with boundary, subject to a non-trivial quadratic constraint. In the present paper, suitable regularity and boundary conditions are imposed for the existence of global solutions. We seek regular solutions with multiple distinct asymptotic $Ad{S}_4\times S^7$ regions, but find that, remarkably, such solutions invariably reduce to multiple covers of the M-Janus solution found by the authors in [arXiv:0904.3313], suggesting rigidity of the half-BPS M-Janus solution. In particular, we prove analytically that no other smooth deformations away from the M-Janus solution exist, as such deformations invariably violate the quadratic constraint. These rigidity results are contrasted to the existence of half-BPS solutions with non-trivial 4-form fluxes and charges asymptotic to $Ad{S}_7\times S^4$. The results are related to the possibility of M2-branes to end on M5-branes, but the impossibility of M5-branes to end on M2-branes, and to the non-existence of half-BPS solutions with simultaneous $Ad{S}_4\times S^7$ and $Ad{S}_7\times S^4$ asymptotic regions.

arXiv comment52 pages, 2 figures, pdf-latex. Minor changes

References in corpus (32)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Large N Field Theories, String Theory and Gravity
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Bubbling AdS space and 1/2 BPS geometries
• Open P-Branes
• Covariant Action for the Super-Five-Brane of M-Theory
• World-Volume Action of the M Theory Five-Brane
• Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus
• Supersymmetric Gauge Theories and the AdS/CFT Correspondence
• A Dilatonic Deformation of AdS_5 and its Field Theory Dual
• Covariant Field Equations of the M Theory Five-Brane
• Exact half-BPS Type IIB interface solutions II: Flux solutions and multi-Janus
• Branes in AdS and pp-wave spacetimes
• Gravity duals of half-BPS Wilson loops
• 1/2-BPS states in M theory and defects in the dual CFTs
• Supersymmetry of Rotating Branes
• Exact Half-BPS Flux Solutions in M-theory I, Local Solutions
• Bubbling Geometries for Half BPS Wilson lines
• Brane Surgery
• M Theory on AdS_p x S^{11-p} and Superconformal Field Theories
• Particles on AdS_{4/7} and Primary Operators on M_{2/5} Brane Worldvolumes
• Janus solutions in M-theory
• Exact Half-BPS Flux Solutions in M-theory II: Global solutions asymptotic to AdS_7 x S^4
• New supersymmetric AdS_3 solutions
• Half-BPS supergravity solutions and superalgebras
• AdS Solutions Through Transgression
• Brane intersections, anti-de Sitter spacetimes and dual superconformal theories
• AdS/CFT dualities involving large 2d N=4 superconformal symmetry

Cited by in corpus (18)

• Near-horizon solutions for D3-branes ending on 5-branes
• Half-BPS Solutions locally asymptotic to AdS_3 x S^3 and interface conformal field theories
• Exact Half-BPS Flux Solutions in M-theory II: Global solutions asymptotic to AdS_7 x S^4
• M-theory Solutions Invariant under $D(2,1;\gamma )\oplus D(2,1;\gamma )$
• Holographic duals of Boundary CFTs
• Exact half-BPS string-junction solutions in six-dimensional supergravity
• Boundary entropy of supersymmetric Janus solutions
• Holographic RG-flows and Boundary CFTs
• Open Worldsheets for Holographic Interfaces
• Exact Half-BPS Flux Solutions in M-theory with $D(2,1;c^{\prime };0{)}^2$ Symmetry: Local Solutions
• Supersymmetric Janus solutions of dyonic $ISO(7)$-gauged $\mathcal{N}=8$ supergravity
• String Junctions and Holographic Interfaces
• Local gravitational solutions dual to M2-branes intersecting and/or ending on M5-branes
• Relating Conifold Geometries to NS5-branes
• AdS-Sliced Flavor Branes and Adding Flavor to the Janus Solution
• Lifshitz-like Janus Solutions
• Rigidity of SU(2,2|2)-symmetric solutions in Type IIB
• $SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs