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

Understand

We simplify and extend the construction of half-BPS solutions to 11-dimensional supergravity, with isometry superalgebra D(2,1;\gamma) \oplus D(2,1;\gamma).

• Their space-time has the form AdS_3 x S^3 x S^3 warped over a Riemann surface \Sigma.
• 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 (\gamma, h, G), where \gamma is the real parameter of the isometry superalgebra, and h and G are functions on \Sigma whose differential equations and regularity conditions depend only on the sign of \gamma.