Exact half-BPS flux solutions in M-theory I local solutionsTo cite this article: Eric D'Hoker et al JHEP08(2008) Abstract: The complete eleven-dimensional supergravity solutions with 16 supersymmetries on manifolds of the form AdS 3 × S 3 × S 3 × Σ, with isometry SO(2, 2) × SO(4) × SO(4), and with either AdS 4 × S 7 or AdS 7 × S 4 boundary behavior, are obtained in exact form. The two-dimensional parameter space Σ is a Riemann surface with boundary, over which the product space AdS 3 × S 3 × 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 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 AdS 3 × S 3 × S 3 , and include fully back-reacted M2-branes in AdS 7 × S 4 and M5-branes in AdS 4 × S 7 . No interpolating solutions exist with mixed AdS 4 × S 7 and AdS 7 × S 4 boundary behavior. Global regularity of these local solutions, as well as the existence of further solutions with neither AdS 4 × S 7 nor AdS 7 × S 4 boundary behavior will be studied elsewhere.

Type IIB superstring theory has AdS 3 × S 3 × M 4 (where the manifold M 4 is either K 3 or T 4 ) solutions which preserve sixteen supersymmetries. In this paper we consider half-BPS solutions which are locally asymptotic to AdS 3 ×S 3 ×M 4 and preserve eight of the sixteen supersymmetries. We reduce the BPS equations and the Bianchi identity for the self-dual five-form field to a set of four differential equations. The complete local solution can be parameterized in terms of two harmonic and two holomorphic functions and all bosonic fields have explicit expressions in terms of these functions.We analyze the conditions for global regularity and construct new half-BPS Janussolutions which have two asymptotic AdS 3 regions. In addition, our analysis proves the global regularity of a class of solutions with more than two asymptotic AdS 3 regions.Finally, we discuss the dual interpretation of the half-BPS Janus solutions carrying only Ramond-Ramond three-form charge as supersymmetric interface theories.

We present a one-parameter deformation of the AdS 4 × S 7 vacuum, which is a regular solution in M-theory, invariant under SO(2, 2) × SO(4) × SO(4), and which preserves 16 supersymmetries. The solution corresponds to a holographic realization of a Janus-like interface/defect theory, despite the absence of a dilaton in M-theory. The 2+1-dimensional CFT dual results from the maximally symmetric CFT through the insertion of a dimension 2 operator which is localized along a 1+1-dimensional linear interface/defect, thereby partially breaking the superconformal symmetry. The solution admits a regular ABJM reduction to a quotient solution which is invariant under SO(2, 2) × SO(4) × U (1) 2 , preserves 12 supersymmetries, and provides a Januslike interface/defect solution in ABJM theory.

We establish a correspondence between certain Lie superalgebras with 16 fermionic generators, and half-BPS solutions to supergravities with 32 supersymmetries. Three cases are discussed. For Type IIB supergravity, we relate semi-simple Lie superalgebras H with 16 fermionic generators which are subalgebras of P SU (2, 2|4), to families of half-BPS solutions which are invariant under H, and locally asymptotic to AdS 5 × S 5 . Similarly, for M-theory, we relate semi-simple Lie superalgebras H with 16 fermionic generators which are subalgebras of OSp(8 * |4) or OSp(8|4, R) to families of half-BPS solutions which are invariant under H, and locally asymptotic to AdS 7 ×S 4 or AdS 4 ×S 7 respectively. Possible enhancements to more than 16 supersymmetries, such as 24, are also analyzed. The classification of semi-simple subalgebras of P SU (2, 2|4), OSp(8 * |4), and OSp(8|4, R) derived in this paper, leads us to conjecture the existence of various new families of half-BPS solutions to Type IIB supergravity and M-theory.

General local half-BPS solutions in M-theory, which have SO(2, 2)× SO(4)× SO(4) symmetry and are asymptotic to AdS 7 × S 4 , were constructed in exact form by the authors in [arXiv:0806.0605]. In the present paper, suitable regularity conditions are imposed on these local solutions, and corresponding globally well-defined solutions are explicitly constructed. The physical properties of these solutions are analyzed, and interpreted in terms of the gravity duals to extended 1+1-dimensional half-BPS defects in the 6-dimensional CFT with maximal supersymmetry.