2008/06/30 by Eric D'Hoker, John Estes, Michael Gutperle +1 · 2 citations
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1088/1126-6708/2008/08/028
published as JHEP 0808:028,2008 · 62 pages, 2 figures, references and clarifications on supergroups added
arxiv created 2008/07/28 · arxiv updated 2014/11/18
The complete eleven-dimensional supergravity solutions with 16 supersymmetries on manifolds of the form AdS3 × S3 × S3 × Σ, with isometry SO(2,2) × SO(4) × SO(4), and with either AdS4 × S7 or AdS7 × S4 boundary behavior, are obtained in exact form. The two-dimensional parameter space Σ is a Riemann surface with boundary, over which the product space AdS3 × S3 × S3 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 Σ, and an integral transform of two further harmonic functions on Σ. 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 AdS3 × S3 × S3, and include fully back-reacted M2-branes in AdS7 × S4 and M5-branes in AdS4 × S7. No interpolating solutions exist with mixed AdS4 × S7 and AdS7 × S4 boundary behavior. Global regularity of these local solutions, as well as the existence of further solutions with neither AdS4 × S7 nor AdS7 × S4 boundary behavior will be studied elsewhere.