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Towards Axion Monodromy Inflation with Warped KK-Modes
High Energy Physics - Theory · Submitted 14 Dec 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim While we have to leave this crucial issue to future studies, we find it interesting that such a simple and explicit stringy monodromy model allows an originally sub-Planckian axion to go through many periods with full quantitative control before back-reaction becomes strong.
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The abstract, sentence by sentence
We present a particularly simple model of axion monodromy: Our axion is the lowest-lying KK-mode of the RR-2-form-potential $C_2$ in the standard Klebanov-Strassler throat. One can think of this inflaton candidate as being defined by the integral of $C_2$ over the $S^2$ cycle of the throat. It obtains an exponentially small mass from the IR-region in which the $S^2$ shrinks to zero size both with respect to the Planck scale and the mass scale of local modes of the throat. Crucially, the $S^2$ cycle has to be shared between two throats, such that the second locus where the $S^2$ shrinks is also in a warped region. Well-known problems like the potentially dangerous back-reaction of brane/antibrane pairs and explicit supersymmetry breaking are not present in our scenario. However, the inflaton back-reaction starts to deform the geometry strongly once the field excursion approaches the Planck scale. We derive the system of differential equations required to treat this effect quantitatively. Numerical work is required to decide whether back-reaction makes the model suitable for realistic inflation. While we have to leave this crucial issue to future studies, we find it interesting that such a simple and explicit stringy monodromy model allows an originally sub-Planckian axion to go through many periods with full quantitative control before back-reaction becomes strong. Also, the mere existence of our ultra-light throat mode (with double exponentially suppressed mass) is noteworthy.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a particularly simple model of axion monodromy: Our axion is the lowest-lying KK-mode of the RR-2-form-potential $C_2$ in the standard Klebanov-Strassler throat. | contribution 0.98 | 0.84 | 0.11 | asserted 1.00 |
| s1 | One can think of this inflaton candidate as being defined by the integral of $C_2$ over the $S^2$ cycle of the throat. | contribution 0.63 | 0.34 | 0.04 | hedged possibility 0.75 |
| s2 | It obtains an exponentially small mass from the IR-region in which the $S^2$ shrinks to zero size both with respect to the Planck scale and the mass scale of local modes of the throat. | result 0.83 | 0.60 | 0.07 | asserted 1.00 |
| s3 | Crucially, the $S^2$ cycle has to be shared between two throats, such that the second locus where the $S^2$ shrinks is also in a warped region. | contribution 0.51 | 0.49 | 0.05 | asserted 1.00 |
| s4 | Well-known problems like the potentially dangerous back-reaction of brane/antibrane pairs and explicit supersymmetry breaking are not present in our scenario. | result 0.76 | 0.52 | 0.09 | asserted 1.00 |
| s5 | However, the inflaton back-reaction starts to deform the geometry strongly once the field excursion approaches the Planck scale. | limitation 0.83 | 0.71 | 0.12 | asserted 0.91 |
| s6 | We derive the system of differential equations required to treat this effect quantitatively. | method 0.74 | 0.94 | 0.04 | asserted 0.99 |
| s7 | Numerical work is required to decide whether back-reaction makes the model suitable for realistic inflation. | future work 0.62 | 0.30 | 0.09 | asserted 0.85 |
| s8 | While we have to leave this crucial issue to future studies, we find it interesting that such a simple and explicit stringy monodromy model allows an originally sub-Planckian axion to go through many periods with full quantitative control before back-reaction becomes strong. | interpretation 0.68 | 0.91 | 0.46 | asserted 0.98 |
| s9 | Also, the mere existence of our ultra-light throat mode (with double exponentially suppressed mass) is noteworthy. | interpretation 0.56 | 0.70 | 0.11 | asserted 0.99 |
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The paper
Original abstract
We present a particularly simple model of axion monodromy: Our axion is the lowest-lying KK-mode of the RR-2-form-potential $C_2$ in the standard Klebanov-Strassler throat. One can think of this inflaton candidate as being defined by the integral of $C_2$ over the $S^2$ cycle of the throat. It obtains an exponentially small mass from the IR-region in which the $S^2$ shrinks to zero size both with respect to the Planck scale and the mass scale of local modes of the throat. Crucially, the $S^2$ cycle has to be shared between two throats, such that the second locus where the $S^2$ shrinks is also in a warped region. Well-known problems like the potentially dangerous back-reaction of brane/antibrane pairs and explicit supersymmetry breaking are not present in our scenario. However, the inflaton back-reaction starts to deform the geometry strongly once the field excursion approaches the Planck scale. We derive the system of differential equations required to treat this effect quantitatively. Numerical work is required to decide whether back-reaction makes the model suitable for realistic inflation. While we have to leave this crucial issue to future studies, we find it interesting that such a simple and explicit stringy monodromy model allows an originally sub-Planckian axion to go through many periods with full quantitative control before back-reaction becomes strong. Also, the mere existence of our ultra-light throat mode (with double exponentially suppressed mass) is noteworthy.
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References
How the literature uses it
20 arXiv papers cite this in 29 sentences
Papers citing it · 15 sentences without a confident label
Builds on it 1 paper
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In this paper, we present a novel type of ultralight axion which, as we argue, is generically present in the type IIB part of the landscape, building on a proposal made in [ref] .
Thraxions: Ultralight Throat Axions · Introduction · 0.98
Compares with it 1 paper
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In this sense, our axion can be made approximately Planckian. * The mass of the axion is $𝒪(w_^3)$ which is parametrically smaller than both the warped Kaluza-Klein scale ($𝒪(w_)$), and the estimate of [ref] , where backreaction of the local geometry was not taken into account ($𝒪(w_^2)$).
Thraxions: Ultralight Throat Axions · Discussion of Results · 0.92
Cites it as background 11 papers
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The Weak Gravity Conjecture (WGC) [ref] (see [ref] for some recent work on this) states that given a $U(1)$ symmetry with gauge coupling $g$, there must exist a particle of charge $q$ and mass $m$ which satisfies the inequality g q M_p ≥m .
Scalar Fields, Hierarchical UV/IR Mixing and The Weak Gravity Conjecture · The Weak Gravity Conjecture and UV/IR Mixing · 0.99
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Of particular interest are axions with monodromic potentials, which spontaneously break shift symmetry and have been proposed to serve as the inflaton [ref] .
Cosmic Microwave Background Dipole Asymmetry could be explained by Axion Monodromy Cosmic Strings · Introduction · 0.95
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Axion monodromy is one of the most promising proposals to achieve transplanckian field ranges in string theory [ref] (see also [ref] ).
Backreaction Issues in Axion Monodromy and Minkowski 4-forms · Introduction · 0.96
What it cites · 45 sentences without a confident label
Uses the method or tool of 4 papers
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Inserting a $4d$ plane wave ansatz $ϕ(x,y)=e^ipx χ(y)$ with $p^2=-m^2$ the equations of motion take the form [equation] which can be brought into the form of a 1d Schrödinger equation [ref] (we follow explicitly [ref] ) [equation] with $z≡e^-ky$, $χ=z^3/2f$, $E=m^2/k^2$ and potential [equation] where $z_IR=1$ and $z_UV=e^-k L$.
An Alternative to Compactification · KK-Reduction on the Effective 5d-Throat and the 4d Action · 0.86
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Inserting a $4d$ plane wave ansatz $ϕ(x,y)=e^ipx χ(y)$ with $p^2=-m^2$ the equations of motion take the form [equation] which can be brought into the form of a 1d Schrödinger equation [ref] (we follow explicitly [ref] ) [equation] with $z≡e^-ky$, $χ=z^3/2f$, $E=m^2/k^2$ and potential [equation] where $z_IR=1$ and $z_UV=e^-k L$.
Tachyons in Throat Cosmology · KK-Reduction on the Effective 5d-Throat and the 4d Action · 0.86
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We now treat the throat as an effectively 5-dimensional Randall-Sundrum-model [ref] .
A Large Mass Hierarchy from a Small Extra Dimension · KK-Reduction on the Effective 5d-Throat and the 4d Action · 0.92
Uses data or values from 1 paper
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The most recent observational constraint by BICEP2 and the Keck Array on the tensor-to-scalar ratio is $r≤0.07$ at 95 % confidence [ref] , which is compatible with large-field inflation.
BICEP2 / Keck Array VI: Improved Constraints On Cosmology and Foregrounds When Adding 95 GHz Data From Keck Array · Introduction · 0.91
Compares with 3 papers
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Using the 4d-Planck mass [ref] [equation] one immediately sees the double exponential suppression of the bound-mode: [equation] Note that this agrees with the expression for the axion-potential in equation (4.76) of [ref] where the potential comes from the NS5-DBI-action.
A Large Mass Hierarchy from a Small Extra Dimension · KK-Reduction on the Effective 5d-Throat and the 4d Action · 0.83
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Using the 4d-Planck mass [ref] [equation] one immediately sees the double exponential suppression of the bound-mode: [equation] Note that this agrees with the expression for the axion-potential in equation (4.76) of [ref] where the potential comes from the NS5-DBI-action.
Gravity Waves and Linear Inflation from Axion Monodromy · KK-Reduction on the Effective 5d-Throat and the 4d Action · 0.83
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The monodromy arises due to the homological triviality of the 2-cycle similar to models proposed in [ref] , rather than due to a coupling to branes.
F-term Axion Monodromy Inflation · Conclusion · 0.80
Cites as support 2 papers
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Back-reaction effects however generically lead to a flattening of the potential [ref] such that the model may well be in accord with current data.
Simple exercises to flatten your potential · Conclusion · 0.99
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Back-reaction effects however generically lead to a flattening of the potential [ref] such that the model may well be in accord with current data.
The Powers of Monodromy · Conclusion · 0.99
Cites as background 36 papers
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A monodromy for axions can be induced by couplings to branes [ref] (see [ref] for very recent progress), but also due to background fluxes [ref] (recently established in the supergravity context under the name of $F$-term axion monodromy inflation [ref] ).
D6-branes and axion monodromy inflation · Introduction · 0.84
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A monodromy for axions can be induced by couplings to branes [ref] (see [ref] for very recent progress), but also due to background fluxes [ref] (recently established in the supergravity context under the name of $F$-term axion monodromy inflation [ref] ).
Gravity Waves and Linear Inflation from Axion Monodromy · Introduction · 0.84
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A monodromy for axions can be induced by couplings to branes [ref] (see [ref] for very recent progress), but also due to background fluxes [ref] (recently established in the supergravity context under the name of $F$-term axion monodromy inflation [ref] ).
Simple exercises to flatten your potential · Introduction · 0.84
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