Beyond LLM in M-theory

The Lin, Lunin, Maldacena (LLM) ansatz in D = 11 supports two independent Killing directions when a general Killing spinor ansatz is considered. Here we show that these directions always commute, identify when the Killing spinors are charged, and show that both their inner product and resulting geometry are governed by two fundamental constants. In particular, setting one constant to zero leads to AdS ₇ × S ⁴, setting the other to zero gives AdS ₄ × S ⁷, while flat spacetime is recovered when both these constants are zero. Furthermore, when the constants are equal, the spacetime is either LLM, or it corresponds to the Kowalski-Glikman solution where the constants are simply the mass parameter.