Quarter-BPS AdS 5 solutions in M-theory with a T 2 bundle over a Riemann surface

A bstract We study and classify quarter-BPS AdS 5 systems in M-theory, whose internal six-dimensional geometry is a T 2 bundle over a Riemann surface and two interval directions. The general system presented, provides a unified description of all known AdS 5 solutions in M-theory. These systems are governed by two functions, one that corresponds to the conformal factor of the Riemann surface and another that describes the T 2 fibration. We find a special set of solutions that can be organized into two classes. In the first one, solutions are specified by the conformal factor of the Riemann surface which satisfies a warped generalization of the SU(∞) Toda equation. The system in the second class requires the Riemann surface to be S 2 , H 2 or T 2 . Class one contains the M-theory AdS 5 solutions of Lin, Lunin and Maldacena; the solutions of Maldacena and Núñez; the solutions of Gauntlett, Martelli, Sparks and Waldram; and the eleven-dimensional uplift of the Y p , q metrics. The second includes the recently found solutions of Beem, Bobev, Wecht and the author. Within each class there are new solutions that will be studied in a companion paper.