Abstract
We discuss quantum gravitational effects in Einstein theory coupled to periodic axion scalars to analyze the viability of several proposals to achieve superplanckian axion periods (aka decay constants) and their possible application to large field inflation models. The effects we study correspond to the nucleation of euclidean gravitational instantons charged under the axion, and our results are essentially compatible with (but independent of) the Weak Gravity Conjecture, as follows: single axion theories with superplanckian periods contain gravitational instantons inducing sizable higher harmonics in the axion potential, which spoil superplanckian inflaton field range. A similar result holds for multi-axion models with lattice alignment (like the Kim-Nilles-Peloso model). Finally, theories with N axions can still achieve a moderately superplanckian periodicity (by a $$ \sqrt{N} $$ factor) with no higher harmonics in the axion potential. The Weak Gravity Conjecture fails to hold in this case due to the absence of some instantons, which are forbidden by a discrete Z N gauge symmetry. Finally we discuss the realization of these instantons as euclidean D-branes in string compactifications.
Highlights
The difficulties in addressing the latter, a sensible approach is to invoke symmetries protecting the model against such corrections; many large-field inflation models are based on axions, i.e. scalars φ with an approximate continuous shift symmetry, broken by non-perturbative effects eiφ/f to a discrete periodicity φ ∼ φ + 2πf
The effects we study correspond to the nucleation of euclidean gravitational instantons charged under the axion, and our results are essentially compatible with the Weak Gravity Conjecture, as follows: single axion theories with superplanckian periods contain gravitational instantons inducing sizable higher harmonics in the axion potential, which spoil superplanckian inflaton field range
4 Gravitational instantons for multiple axions. These bounds on transplanckian decay constants coming from purely quantum gravitational arguments agree with the difficulties found in string theory to provide a transplanckian axion
Summary
We will study the possibility of transplanckian field ranges in a quantum theory of gravity from a semiclassical perspective, focusing on those effects which can be safely described using the Einstein-Hilbert action for the gravitational field. The essence of the WGC can be reduced to the statement that, for any abelian p-form field, there must be a charged p-dimensional object with tension g T√. The rationale for the conjecture is that one expects to be able to build black p − 1 membranes electrically charged under the abelian p-form field. These black branes will generically evaporate via Hawking radiation, radiating their charge away. This is only possible if there is an object lighter than the black brane and with a smaller charge. There are two posssible loopholes to the above conjecture, which we discuss in some detail
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