TL;DR
This paper classifies supersymmetric near horizon geometries in M-theory by solving Killing spinor equations, characterizing horizon sections with Spin(7) structures, and providing explicit solutions and examples.
Contribution
It explicitly solves the Killing spinor equations for M-horizons, characterizes the geometry of horizon sections, and introduces a Lichnerowicz-type theorem linking zero modes to Killing spinors.
Findings
Horizon sections are 9-dimensional manifolds with Spin(7) structure.
A Lichnerowicz-type theorem relates Dirac zero modes to Killing spinors.
Explicit solutions and examples of supersymmetric M-horizons are provided.
Abstract
We solve the Killing spinor equations and determine the near horizon geometries of M-theory that preserve at least one supersymmetry. The M-horizon spatial sections are 9-dimensional manifolds with a Spin(7) structure restricted by geometric constraints which we give explicitly. We also provide an alternative characterization of the solutions of the Killing spinor equation, utilizing the compactness of the horizon section and the field equations, by proving a Lichnerowicz type of theorem which implies that the zero modes of a Dirac operator coupled to 4-form fluxes are Killing spinors. We use this, and the maximum principle, to solve the field equations of the theory for some special cases and present some examples.
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