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The swampland conjecture and the Higgs expectation value
High Energy Physics - Theory · Submitted 4 Oct 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Consequently, we argue that most of the habitable vacua in the string landscape are in tension with the phenomenological constraints.
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The abstract, sentence by sentence
The recently proposed de Sitter swampland conjecture excludes local extrema of a scalar potential with a positive energy density in a low energy effective theory. Under the conjecture, the observed dark energy cannot be explained by the cosmological constant. The local maximum of the Higgs potential at the symmetric point also contradicts with the conjecture. In order to make the Standard Model consistent with the conjecture, it has been proposed to introduce a quintessence field, $Q$, which couples to the cosmological constant and the local maximum of the Higgs potential. In this paper, we show that such a modified Higgs potential generically results in a $Q$-dependent Higgs vacuum expectation value (VEV). The $Q$-dependence of the Higgs VEV induces a long-range force, which is severely excluded by the tests of the equivalence principle. Besides, as the quintessence field is in motion, the Higgs VEV shows a time-dependence, which is also severely constrained by the measurements of the time-dependence of the proton-to-electron mass ratio. Those constraints require an additional fine-tuning which is justified neither by the swampland conjecture nor the anthropic principle. We further show that, even if such an unjustified fine-tuning condition is imposed at the tree level, radiative corrections upset it. Consequently, we argue that most of the habitable vacua in the string landscape are in tension with the phenomenological constraints.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The recently proposed de Sitter swampland conjecture excludes local extrema of a scalar potential with a positive energy density in a low energy effective theory. | background 1.00 | 0.03 | 0.03 | asserted 0.94 |
| s1 | Under the conjecture, the observed dark energy cannot be explained by the cosmological constant. | background 0.98 | 0.06 | 0.04 | asserted 0.99 |
| s2 | The local maximum of the Higgs potential at the symmetric point also contradicts with the conjecture. | background 0.99 | 0.09 | 0.03 | asserted 0.99 |
| s3 | In order to make the Standard Model consistent with the conjecture, it has been proposed to introduce a quintessence field, $Q$, which couples to the cosmological constant and the local maximum of the Higgs potential. | background 0.98 | 0.05 | 0.03 | asserted 0.84 |
| s4 | In this paper, we show that such a modified Higgs potential generically results in a $Q$-dependent Higgs vacuum expectation value (VEV). | result 0.67 | 0.93 | 0.08 | asserted 1.00 |
| s5 | The $Q$-dependence of the Higgs VEV induces a long-range force, which is severely excluded by the tests of the equivalence principle. | result 0.93 | 0.42 | 0.10 | asserted 1.00 |
| s6 | Besides, as the quintessence field is in motion, the Higgs VEV shows a time-dependence, which is also severely constrained by the measurements of the time-dependence of the proton-to-electron mass ratio. | result 0.96 | 0.25 | 0.05 | asserted 1.00 |
| s7 | Those constraints require an additional fine-tuning which is justified neither by the swampland conjecture nor the anthropic principle. | interpretation 0.76 | 0.49 | 0.12 | asserted 1.00 |
| s8 | We further show that, even if such an unjustified fine-tuning condition is imposed at the tree level, radiative corrections upset it. | result 0.94 | 0.91 | 0.09 | asserted 1.00 |
| s9 | Consequently, we argue that most of the habitable vacua in the string landscape are in tension with the phenomenological constraints. | interpretation 0.94 | 0.57 | 0.82 | asserted 0.49 |
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The paper
Original abstract
The recently proposed de Sitter swampland conjecture excludes local extrema of a scalar potential with a positive energy density in a low energy effective theory. Under the conjecture, the observed dark energy cannot be explained by the cosmological constant. The local maximum of the Higgs potential at the symmetric point also contradicts with the conjecture. In order to make the Standard Model consistent with the conjecture, it has been proposed to introduce a quintessence field, $Q$, which couples to the cosmological constant and the local maximum of the Higgs potential. In this paper, we show that such a modified Higgs potential generically results in a $Q$-dependent Higgs vacuum expectation value (VEV). The $Q$-dependence of the Higgs VEV induces a long-range force, which is severely excluded by the tests of the equivalence principle. Besides, as the quintessence field is in motion, the Higgs VEV shows a time-dependence, which is also severely constrained by the measurements of the time-dependence of the proton-to-electron mass ratio. Those constraints require an additional fine-tuning which is justified neither by the swampland conjecture nor the anthropic principle. We further show that, even if such an unjustified fine-tuning condition is imposed at the tree level, radiative corrections upset it. Consequently, we argue that most of the habitable vacua in the string landscape are in tension with the phenomenological constraints.
Human review
References
How the literature uses it
35 arXiv papers cite this in 44 sentences
Papers citing it · 27 sentences without a confident label
Contests it 2 papers
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Since there appear to be a number of counter-examples [ref] , several authors subsequently proposed a refined version of the conjecture [ref] , which states that the inequality should only hold unless the minimal eigenvalue of the Hessian is bounded from above, $min(∇_i∇_j V) ≤-c^'V$, where $c^'>0$ is another $𝒪(1)$ number (see also [ref] for other proposals).
Weakly Coupled de Sitter Vacua with Fluxes and the Swampland · Introduction · contest 0.72
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([ref]) does not only forbid the de-Sitter minima but also the de-Sitter maxima as well, and several counter examples were known [ref] or have been reported soon after the proposal was made [ref] reflecting the need of refining the de-Sitter swampland conjecture in eqn.
$T$-dualizing the de-Sitter no-go scenarios · Introduction · contest 0.77
Cites it as background 15 papers
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After the initial proposal [ref] , some bottom-up constraints of the conjecture has been pointed out in Refs. [ref] , leading to several proposals for refinements [ref] .
Is Gravity the Weakest Force? · Introduction · 0.98
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Indeed, the refined dS conjecture [ref] as part of the Swampland program [ref] posits that long periods of accelerated cosmological expansion are severely limited in quantum gravity and metastable dS minima are forbidden in asymptotic regions of the moduli space (the earlier, stronger dS conjecture [ref] required modification due to explicit counter-examples [ref] ).
Heterotic de Sitter Beyond Modular Symmetry · Introduction · 0.90
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Recently there has been a revived interest in dS vacua in string theory due to the so called dS swampland conjecture [ref] , that says that there are no dS vacua in string theory.[This renewed interest in the topic has led to a surge of new papers, see for example [ref] .] While currently quintessence models with for example simple exponential potentials provide an observationally viable alternative to dS vacua [ref] , it is unclear whether such models are easier to construct in string theory than dS vacua [ref] .
Scaling limits of dS vacua and the swampland · Introduction · 0.92
What it cites · 28 sentences without a confident label
Uses the method or tool of 4 papers
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Here, we again utilize SMH [ref] to obtain $v_H^()(X≠0)$ for given $λ^()(X≠0)$ and $M_H^2()(X≠0)$.
Higgs boson mass in the Standard Model at two-loop order and beyond · Analysis in the $$ prescription · 1.00
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Following Refs. [ref] , we define the $$ VEV, $v_H^()(X)$, by the field value of $h$ which minimizes $V_Heff$ in the $$ prescription.
The Standard Model Effective Potential at Two Loops · Analysis in the $$ prescription · 0.93
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Following Refs. [ref] , we define the $$ VEV, $v_H^()(X)$, by the field value of $h$ which minimizes $V_Heff$ in the $$ prescription.
Three-loop Standard Model effective potential at leading order in strong and top Yukawa couplings · Analysis in the $$ prescription · 0.93
Uses data or values from 5 papers
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The coupling of the quintessence field to the quarks leads to its coupling to the nucleons [ref] , [equation] where $m_N$ is the nucleon mass, and $f_N$ is defined as [equation] with [equation] In the following, we use the scalar coupling estimated by using phenomenological and lattice QCD calculations [ref] , [equation] The isospin violating effect is also estimated to be, [equation] with an $O(10)$% accuracy [ref] .
Improved limits for Higgs-portal dark matter from LHC searches · Constraints on the quintessence dependent Higgs VEV · 0.88
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The coupling of the quintessence field to the quarks leads to its coupling to the nucleons [ref] , [equation] where $m_N$ is the nucleon mass, and $f_N$ is defined as [equation] with [equation] In the following, we use the scalar coupling estimated by using phenomenological and lattice QCD calculations [ref] , [equation] The isospin violating effect is also estimated to be, [equation] with an $O(10)$% accuracy [ref] .
Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: Disentangling two- and three-flavor effects · Constraints on the quintessence dependent Higgs VEV · 0.88
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We first calculate $v_H^()(X=0)$ at $μ_R = m_t^(pole)$ from the relation between $v_H^()(X=0)$ and the Fermi coupling constant $G_μ$ in [ref] , which leads to [A nominal uncertainty, $v_H^()(X=0) = 246.7711±0.0015$ ($μ_R = m_top^(pole)$), is dominated by the error of the top quark mass, $m_t^(pole) = 173.0 ±0.4$ GeV [ref] , although we do not need a very precise value of it. ] [equation] Then, we obtain the quartic coupling and the Higgs mass parameters at $X=0$, [equation] at $μ_R = m_t^(pole)$.
Higgs mass and vacuum stability in the Standard Model at NNLO · Analysis in the $$ prescription · 0.85
Cites as support 6 papers
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This assumption is motivated by the fact that the $Q$-dependences of them are severely constrained by the tests of the equivalence principle, by the test of the time-variation of the fundamental couplings, and by the BBN constraints [ref] .
Nucleosynthesis and the Time Dependence of Fundamental Couplings · Wilsonian approach · 0.99
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This assumption is motivated by the fact that the $Q$-dependences of them are severely constrained by the tests of the equivalence principle, by the test of the time-variation of the fundamental couplings, and by the BBN constraints [ref] .
Torsion-balance tests of the weak equivalence principle · Wilsonian approach · 0.99
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This assumption is motivated by the fact that the $Q$-dependences of them are severely constrained by the tests of the equivalence principle, by the test of the time-variation of the fundamental couplings, and by the BBN constraints [ref] .
The status of varying constants: a review of the physics, searches and implications · Wilsonian approach · 0.99
Cites as background 40 papers
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Among various conjectures, the most recent one [ref] , the so-called de Sitter swampland conjecture, stimulates intensive studies of its phenomenological and cosmological consequences [ref] .
Isocurvature Perturbations of Dark Energy and Dark Matter from the Swampland Conjecture · Introduction · 0.95
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Among various conjectures, the most recent one [ref] , the so-called de Sitter swampland conjecture, stimulates intensive studies of its phenomenological and cosmological consequences [ref] .
New Scalar Field Quartessence · Introduction · 0.95
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Among various conjectures, the most recent one [ref] , the so-called de Sitter swampland conjecture, stimulates intensive studies of its phenomenological and cosmological consequences [ref] .
Constraints on the sum of the neutrino masses in dynamical dark energy models with $w(z) \geq -1$ are tighter than those obtained in $\Lambda$CDM · Introduction · 0.95
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