On the generality of the LLM geometries in M-theory
Eoin \'O Colg\'ain, Jun-Bao Wu, Hossein Yavartanoo
TL;DR
This paper investigates the LLM class of supergravity solutions in M-theory, proving that no additional supersymmetric geometries with extra fluxes exist beyond the known ansatz, and clarifies the relationship between Killing spinors.
Contribution
It generalizes the LLM solutions by allowing all fluxes consistent with symmetries and proves the uniqueness of the supersymmetric geometries within this class.
Findings
No supersymmetric geometries with additional fluxes beyond LLM.
The relationship between Killing spinors is derived from symmetry considerations.
Clarifies the structure of R-symmetry directions in these solutions.
Abstract
In this note we revisit the Lin, Lunin, Maldacena (LLM) class of d=11 supergravity solutions with symmetry SO(6) X SO(3) X R, but generalise to allow for all fluxes consistent with the isometries. Using the Killing spinor equation, we prove there are no supersymmetric geometries with additional fluxes beyond the LLM ansatz. In addition, the LLM relationship between Killing spinors, \epsilon_- = - \gamma_5 \epsilon_+, may be seen as a consequence of identifying two Killing directions identified through the Killing spinor equation corresponding to candidate R-symmetry directions.
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