Beyond LLM in M-theory

TL;DR

This paper explores the geometric and algebraic properties of the LLM ansatz in M-theory, revealing how fundamental constants determine various known solutions like AdS spaces and flat spacetime.

Contribution

It identifies the conditions under which Killing directions commute, characterizes when Killing spinors are charged, and links constants to specific M-theory solutions.

Findings

Constants determine AdS7 x S4 and AdS4 x S7 solutions.

Killing directions always commute under the ansatz.

Flat spacetime is recovered when both constants are zero.

Abstract

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 AdS7 x S4, setting the other to zero gives AdS4 x S7, 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.