Transplanckian axions !? (1503.03886v2)

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 $\mathbf{Z}_N$ gauge symmetry. Finally we discuss the realization of these instantons as euclidean D-branes in string compactifications.

• The paper demonstrates that gravitational instantons impose significant quantum corrections that prevent single axion models from reaching transplanckian field ranges.
• It explores both single and multi-axion frameworks, revealing the role of discrete gauge symmetries and higher harmonics in modulating axion potentials.
• The study aligns with a generalized Weak Gravity Conjecture, underscoring constraints on large field inflation while hinting at string-theoretical applications via D-brane instantons.

An Analysis of Transplanckian Axions and Gravitational Instantons

The paper by Montero, Uranga, and Valenzuela investigates the quantum gravitational effects in scenarios where Einstein's theory is coupled to periodic axion scalars, specifically focusing on the possibility of achieving axion decay constants that are superplanckian. This is done with the context of axion models' application in large field inflation. The work essentially discerns the limitations imposed by gravitational instantons and evaluates the viability of axion models with superplanckian decay constants, either through single or multiple axion models.

The analysis centers on gravitational instantons, specifically Euclidean gravitational instantons that are charged under axions. These configurations potentially generate additional harmonics in the axion potential, which significantly impact the feasibility of superplanckian inflationary field ranges. When considering single axion theories with superplanckian periods, it is shown that the gravitational instantons prevent the desired transplanckian inflaton field ranges, contradicting the notion that such periods may not encounter quantum gravitational corrections.

For multi-axion systems, like those employing lattice alignment or kinetic alignment, the results vary. Lattice alignment forms like the Kim-Nilles-Peloso model allow the introduction of moderately enhanced axion decay constants. However, these are still subject to the resonance of harmonics, posing similar issues as in single axion models. In contrast, it is noted that models with $N$ axions balanced by a discrete $Z_N$ gauge symmetry could theoretically achieve a moderately superplanckian period by selectively witnessing the absence of specific higher harmonics in the potential.

Importantly, the paper aligns with the Weak Gravity Conjecture (WGC), which argues that sufficiently strong additional instanton effects must limit transplanckian field variations in any coherent theory incorporating quantum gravity. However, the authors suggest a generalization of WGC that accommodates the effects of a discrete gauge symmetry as an additional moderating factor.

The implication of their analysis, especially in a multi-axion framework, extends to the field of realizing string compactifications involving D-branes. D-brane instantons appear in the discussion as potential string solutions to nonperturbative effects, closely paralleling gravitational instantons. In scenarios of natural or aligned inflation in string theory, Euclidean D-branes play a role akin to the gravitational instantons, revealing how they modulate the axion potential while also respecting the discrete symmetry.

The outcomes suggest that the pursuit of transplanckian axion potentials is fraught with complex interplays including contributions from both quantum gravity corrections and discretized gauge symmetries. While the existence of NI axions maintains a viable theoretical base for large field ranges, reservations persist about achieving viable transplanckian models without encountering substantial superpotentials that could disrupt the flatness required for successful inflation.

Montero, Uranga, and Valenzuela’s paper highlights the multifaceted complexities crucial to advancing unified theories in high-energy physics and cosmology. It sharpens the focus on the intrinsic limitations posed by gravity and symmetry, essential for conceptualizing physics beyond the standard model, upholding consistency with principles entailed by the Weak Gravity Conjecture, and reinforcing the tenability of large field inflation within a framework inclusive of string theory. Future insights may necessitate the deep integration of these findings to expand the frontier of cosmological model-building, especially in dimensions governed by quantum gravitational physics.