1/4-BPS M-theory bubbles with SO(3) × SO(4) symmetry

In this paper we generalize the work of Lin, Lunin and Maldacena on the classification of 1/2-BPS M-theory solutions to a specific class of 1/4-BPS configurations. We are interested in the solutions of 11 dimensional supergravity with SO(3) × SO(4) symmetry, and it is shown that such solutions are constructed over a one-parameter familiy of 4 dimensional almost Calabi-Yau spaces. Through analytic continuations we can obtain M-theory solutions having AdS2 × S 3 or AdS3 × S 2 factors. It is shown that our result is equivalent to the AdS solutions which have been recently reported as the near-horizon geometry of M2 or M5-branes wrapped on 2 or 4-cycles in Calabi-Yau threefolds. We also discuss the hierarchy of M-theory bubbles with different number of supersymmetries.