The purpose of this paper is two-fold. First we review in detail the geometric aspects of the swampland program for supersymmetric 4d effective theories using a new and unifying language we dub "domestic geometry", the generalization of special Kahler geometry which does not require the underlying manifold to be Kahler or have a complex structure. All 4d SUGRAs are described by domestic geometry. As special Kahler geometries, domestic geometries carry formal brane amplitudes: when the domestic geometry describes the supersymmetric low-energy limit of a consistent quantum theory of gravity, its formal brane amplitudes have the right properties to be actual branes. The main datum of the domestic geometry of a 4d SUGRA is its gauge coupling, seen as a map from a manifold which satisfies the geometric Ooguri-Vafa conjectures to the Siegel variety; to understand the properties of the quantum-consistent gauge couplings we discuss several novel aspects of such "Ooguri-Vafa" manifolds, including their Liouville properties. Our second goal is to present some novel speculation on the extension of the swampland program to non-supersymmetric effective theories of gravity. The idea is that the domestic geometric description of the quantum-consistent effective theories extends, possibly with some qualifications, also to the non-supersymmetric case.

Swampland geometry and the gauge couplings / Cecotti, Sergio. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - :9(2021), pp. 1-68. [10.1007/JHEP09(2021)136]

Swampland geometry and the gauge couplings

Sergio Cecotti
2021

Abstract

The purpose of this paper is two-fold. First we review in detail the geometric aspects of the swampland program for supersymmetric 4d effective theories using a new and unifying language we dub "domestic geometry", the generalization of special Kahler geometry which does not require the underlying manifold to be Kahler or have a complex structure. All 4d SUGRAs are described by domestic geometry. As special Kahler geometries, domestic geometries carry formal brane amplitudes: when the domestic geometry describes the supersymmetric low-energy limit of a consistent quantum theory of gravity, its formal brane amplitudes have the right properties to be actual branes. The main datum of the domestic geometry of a 4d SUGRA is its gauge coupling, seen as a map from a manifold which satisfies the geometric Ooguri-Vafa conjectures to the Siegel variety; to understand the properties of the quantum-consistent gauge couplings we discuss several novel aspects of such "Ooguri-Vafa" manifolds, including their Liouville properties. Our second goal is to present some novel speculation on the extension of the swampland program to non-supersymmetric effective theories of gravity. The idea is that the domestic geometric description of the quantum-consistent effective theories extends, possibly with some qualifications, also to the non-supersymmetric case.
9
1
68
136
10.1007/JHEP09(2021)136
https://arxiv.org/abs/2102.03205
Cecotti, Sergio
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/128634
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