Abstract
The axionic weak gravity conjecture predicts the existence of instantons whose actions are less than their charges in appropriate units. We show that the conjecture is satisfied for the axion-dilaton-gravity system if we assume duality constraints on the higher derivative corrections in addition to positivity bounds which follow from unitarity, analyticity, and locality of UV scattering amplitudes. On the other hand, the conjecture does not follow if we assume the positivity bounds only. This presents an example where derivation of the weak gravity conjecture requires more detailed UV information than the consistency of scattering amplitudes.
Highlights
The Swampland program is based on the premise that there are conditions on a low-energy gravity theory that are necessary in order for it to be an effective theory of a consistent quantum gravity with ultraviolet (UV) completion such as string theory but cannot be derived solely from consistency requirements evident in low energy [1]
We find that the weak gravity conjecture (WGC) for the axion-gravity system follows from unitarity, analyticity, and locality of UV scattering amplitudes
In this paper we showed that the WGC for ð−1Þ-form symmetry in the axion-gravity system follows from the positivity bounds on higher derivative corrections and that in the axion-dilaton-gravity system it follows if we in addition assume certain duality constraints
Summary
The Swampland program is based on the premise that there are conditions on a low-energy gravity theory that are necessary in order for it to be an effective theory of a consistent quantum gravity with ultraviolet (UV) completion such as string theory but cannot be derived solely from consistency requirements evident in low energy [1]. We show that the positivity bounds for the axion-gravity system imply the action-to-charge ratios (1.1) required by the WGC. DUALITY AND AXIONIC WEAK GRAVITY dilaton, together with positivity bounds, does imply the axionic WGC This presents an example where detailed UV information such as duality is needed to demonstrate the conjecture, on top of the positivity bounds which follow from unitarity, analyticity, and locality of UV scattering amplitudes. Some technical details in our derivations can be found in the Appendixes
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