Upper bounds for Fourier transforms of exponential functions

Knockaert, Luc

doi:10.1080/17476933.2010.534787

Cited by 2 publications

(1 citation statement)

References 7 publications

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“…Then, a theorem by [125] C. Furthermore, using the results of [124], we can further relax this assumption to convex functions h(p) that are analytic within a strip | Im p | < c for c > 0. For ease of presentation, though, we will restrict ourselves to simple even-degree polynomials in the text.…”

Section: B Asymptotic Behavior Of the Thermal Partition Functionmentioning

confidence: 99%

Instanton Expansions and Phase Transitions

Stout¹

2020

Preprint

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A central object in any axionic theory is its periodic potential, which is typically generated by instantons. The goal of this paper is to understand what physically happens to the theory when we lose control of the potential's instanton expansion. We argue, using the Yang-Lee theory of phase transitions, that the theory breaks down in the classic sense: states become light. However, these states are not necessarily light for all values of the axion and there can be large regions where the effective description remains valid. We find alternative expressions for the effective potential in terms of the properties of these light states, which remain useful even when the instanton expansion breaks down, and thus initiate a push beyond the lamppost of large instanton actions. Most of these questions are motivated by the axionic Weak Gravity Conjecture, which we reformulate without reference to instanton actions. We also comment on its ability to constrain large-field axion inflation.

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Section: B Asymptotic Behavior Of the Thermal Partition Functionmentioning

confidence: 99%

Instanton Expansions and Phase Transitions

Stout¹

2020

Preprint

View full text Add to dashboard Cite

show abstract

Instanton expansions and phase transitions

Stout

2022

J. High Energ. Phys.

View full text Add to dashboard Cite

A central object in any axionic theory is its periodic potential, which is typically generated by instantons. The goal of this paper is to understand what physically happens to the theory when we lose control of the potential’s instanton expansion. We argue, using the Yang-Lee theory of phase transitions, that the theory breaks down in the classic sense: states become light. However, these states are not necessarily light for all values of the axion and there can be large regions where the effective description remains valid. We find alternative expressions for the effective potential in terms of the properties of these light states, which remain useful even when the instanton expansion breaks down, and thus initiate a push beyond the lamppost of large instanton actions. Most of these questions are motivated by the axionic Weak Gravity Conjecture, which we reformulate without reference to instanton actions. We also comment on its ability to constrain large-field axion inflation.

show abstract

Upper bounds for Fourier transforms of exponential functions

Cited by 2 publications

References 7 publications

Instanton Expansions and Phase Transitions

Instanton Expansions and Phase Transitions

Instanton expansions and phase transitions

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