Abstract
We investigate the consequences of combining swampland conjectures with the requirement of asymptotic safety. To this end, we explore the infrared regime of asymptotically safe gravity in the quadratic one-loop approximation, and we identify the hypersurface spanned by the endpoints of asymptotically safe renormalization group trajectories. These comprise the allowed values of higher-derivative couplings, as well as standard logarithmic form factors. We determine the intersection of this hypersurface with the regions of parameter space allowed by the weak-gravity conjecture, the swampland de Sitter conjecture, and the trans-Planckian censorship conjecture. The latter two depend on some order-one constants, for generic values of which we show that the overlap region is a proper subspace of the asymptotically safe hypersurface. Moreover, the latter lies inside the region allowed by the weak gravity conjecture assuming electromagnetic duality. Our results suggest a non-trivial interplay between the consistency conditions stemming from ultraviolet completeness of the renormalization group flow, black hole physics, and cosmology.
Highlights
The 20th century has seen the development of two pillars of modern theoretical physics: quantum field theory (QFT) and general relativity (GR)
The more stringent and well-grounded swampland proposals, such as the “no global symmetries” [60,61,62,63] and weak gravity [64] conjectures, could help guide the search for asymptotic safety, which is currently faced with the daunting prospect of navigating ever-larger theory spaces [65,66]
Let us stress that our aim is to intersect swampland bounds with the constraints provided by asymptotic safety, and the technical obstacles to compute its consequences for quartic electromagnetic couplings in gravity, which would entail involved FRG computations along the lines of [66], compel us to focus on the duality-invariant scenario of [169], which at any rate appears intriguing on its own5
Summary
The 20th century has seen the development of two pillars of modern theoretical physics: quantum field theory (QFT) and general relativity (GR). Despite remarkable progress in a number of directions, the difficulties of formulating a complete theory of quantum gravity have led a considerable portion of the community to shift the focus on general, possibly model-independent lessons that could shed light on the nature of gravity at all scales Many of these proposals, commonly dubbed “swampland conjectures” [4] in the context of string theory, rest on considerations on black-hole physics, which often can lie entirely in the semi-classical regime where one expects low-energy effective field theory (EFT) to be a reliable description. The more stringent and well-grounded swampland proposals, such as the “no global symmetries” [60,61,62,63] and weak gravity [64] conjectures, could help guide the search for asymptotic safety, which is currently faced with the daunting prospect of navigating ever-larger theory spaces [65,66]
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