Weak <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>G</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> manifolds and scale separation in M-theory from type IIA backgrounds

Abstract

This work provides evidence for the existence of supersymmetric and scale-separated <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mi>AdS</a:mi> </a:mrow> <a:mrow> <a:mn>4</a:mn> </a:mrow> </a:msub> </a:mrow> </a:math> vacua in M-theory of the Freund-Rubin type. The internal space has weak <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>G</c:mi> <c:mn>2</c:mn> </c:msub> </c:math> -holonomy, which is obtained from the lift of AdS (anti–de Sitter) vacua in massless type IIA on a specific SU(3) structure with O6-planes. Such lifts require a local treatment of the O6-planes, therefore going beyond the usual smeared approximation. The setup is analyzed by solving the pure spinor equations and the Bianchi identities perturbatively in a small backreaction parameter, preserving supersymmetry manifestly and therefore extending on previous work. This approach is applicable to lifts of other type IIA vacua on half-flat SU(3) structures, including those with D6-brane sources. The resulting 7D manifold presented here exhibits singularities originating from the O6-planes loci in type IIA theory. Additionally, scale separation in M-theory arises from a decoupling between the Ricci curvature and the first eigenvalue of the Laplacian of the proposed 7D manifold, thereby challenging certain conjectures in the swampland program. Published by the American Physical Society 2024

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