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

TL;DR

This work extends the Lin-Lunin-Maldacena program to 1/4-BPS M-theory bubbles with $SO(3)\times SO(4)$ symmetry by deriving the 6D Killing spinor equations from 11D supergravity and showing the solution space is governed by a 4D almost Calabi-Yau base with an $SU(2)$ structure. Through spinor bilinears, it identifies precise differential constraints that render the 11D geometry as a warped product over ${\cal M}_4$, and demonstrates that analytic continuations yield $AdS_2\times S^3$ and $AdS_3\times S^2$ solutions matching wrapped M2/M5-brane near-horizon geometries. The paper also connects these 1/4-BPS bubbles to known 1/8-BPS AdS bubbles, recasting the problem within an 8D Kahler-base framework and presenting a governing PDE for the Ricci scalar. Overall, it provides a coherent geometric framework for 1/4-BPS sectors in M-theory and clarifies the relationship between different BPS bubbles and their dual field theories.

Abstract

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 $SO(3)\times SO(4)$ 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 $AdS_2\times S^3$ or $AdS_3\times S^2$ 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.