Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant

Joseph Polchinski; Raphael Bousso

REVIEW

Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant

Raphael Bousso, Joseph Polchinski

High Energy Physics - Theory · Submitted 18 Apr 2000 · 52 references

Pith's verdict: The paper that turned the cosmological constant into a discrete landscape variable, and the core argument — flux quantization plus a multi-flux grid — survives rereading; the soft parts are the frozen charges and the qualitative reheating story.

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CitationJoseph Polchinski, Raphael Bousso. "Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant." arXiv:hep-th/0004134 (2000). https://pith.science/paper/2NQAODZ7

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This is the paper that made the cosmological constant a discrete landscape variable, and it holds up better than most foundational papers do on a second read. Two things are actually new. First, the claim that the four-form flux itself — not just its jumps across membranes — is quantized (Eqs. 2.9–2.11), derived from the M5-brane charge in eleven dimensions (2.15–2.18). That is a clean first-principles argument, and it removes the continuous parameter that Hawking and Brown–Teitelboim had leaned on. Second, the observation that with J fluxes the allowed values of lambda form a J-dimensional grid, so a shell of width Delta-lambda contains a grid point once the product of the charges is small enough (2.24–2.26). The volume argument is elementary and correct in its stated regime, and the numbers are honest: of order 100 fluxes at GUT scale, four or five with large extra dimensions. The cosmology is a straightforward extension of Brown–Teitelboim with one useful addition: the de Sitter temperature kicks the inflaton around before the final nucleation, so you do not end up with an empty universe. That is the section I would hand to a student. Soft spots, in order of weight. The frozen, incommensurate charges are assumed, not derived; the authors say so in the introduction and again in 2.3, where they note that V7 is dynamical and the flux energy is really a potential for the volume. The stress-test worry about commensurability lands, but I would rank it lower than it sounds: exact rational relations among radii are non-generic, so the real question is whether stabilization lands on symmetric points, not whether incommensurability is attainable at all. The degeneracy D in 2.5 is genuinely unquantified and could move the required charge by orders of magnitude. And the entropy and perturbation claim in the abstract (s6) rests on Sec. 3.2, which is order-of-magnitude estimates with a threshold like M11/MPl greater than about 10^-1.3 — suggestive, not established. None of this touches the central claim that a dense discretuum exists and can be populated. What the paper delivers is a scenario with the right ingredients, not a derivation of the observed lambda, and it says as much; the anthropic step in 3.3 is explicit rather than smuggled. Read it if you work on the landscape, anthropic selection, or flux compactification. It deserves referee time.

Referee report

Significance

If correct, this paper converts the cosmological constant from a continuous parameter into a discrete landscape variable and supplies a dynamical mechanism for reaching a small value. The quantization derivation (Eqs. 2.15–2.18) is a clean, essentially parameter-free consequence of M5-brane charge, and the density estimate (Eqs. 2.24–2.26) is dimensionally correct and correctly captures the J-dependence, including the useful observation that cancellation becomes easier as |λbare| grows. The paper is candid about its assumptions: the frozen-charge idealization is stated in the Introduction, the dynamical volume is flagged in Sec. 2.3, the unquantified degeneracy D is stated in Sec. 2.5, and the inﬂaton potential is explicitly not derived. It makes a quantitative, checkable statement (J ≈ 100 versus J′ ≈ 4) tied to the extra-dimension scenario, and it correctly presents a residual nonzero λ as a prediction rather than a defect. The anthropic step is explicitly labelled as such.

Major objections (3)

[Sec. 2.3 (footnote 5) and Sec. 2.5] The discretuum argument requires two things that are asserted rather than demonstrated: that the charges q_i² are rationally independent, and that the flat background gauge potentials (the stringy θ-parameters of footnote 5) are fixed. The paper acknowledges the frozen-charge idealization in the Introduction and states that the θ-parameters 'must eventually be stabilized and so the fluxes will in fact take discrete values,' but this is a single sentence carrying the weight of the quantization claim [abstract:s1]. A concrete test would help: in the seven-torus model of Sec. 2.5 the q_i are explicit functions of seven radii, so one could show that the commensurate locus is measure zero and that a generic stabilized point is attainable. A related self-consistency issue deserves an explicit error estimate: Sec. 2.3 notes that V7 is dynamical and depends on n_i, so the q_i in Eq. (2.21) are not exactly fixed, whereas the density estimate (2.24)–(2.26) treats them as fixed. The size of the induced shift in the grid spacing should be stated.
[Secs. 2.5 and 2.6, Eq. (2.44)] The degeneracy D is explicitly left unquantified ('we do not know how to estimate a reasonable degeneracy'), yet it enters the density condition linearly in Eq. (2.25) and therefore the required charge as D^{1/J}. For J ≈ 100 this is harmless, but for the J′ = 4 large-dimension case of Eq. (2.44) it enters as D^{1/8}; a degeneracy of 10⁸, which is not implausible given the E7(7) U-duality the paper itself raises in Sec. 2.5, would relax the bound on M11 by a factor of order 10 and change the quantitative claim that 'four or five four-forms suffice.' The D-dependence should be propagated explicitly in Sec. 2.6 rather than absorbed into an assumption that D is small.
[Secs. 3.2.2 and 2.6, Eq. (3.12)] The 'kicking the inﬂaton' reheating mechanism requires M11 ≳ 10¹⁷ GeV (Eq. 3.12), whereas the density argument is most attractive in the large-extra-dimension scenario with M11 of order a TeV (Sec. 2.6). The two regimes that make the two halves of the paper work are therefore disjoint, and the fallback in Sec. 3.2.3 is described as 'less generic' and is not worked out beyond a sketch. Since the production of entropy and density perturbations is one of the paper's stated claims [abstract:s6], this tension should be stated plainly in the Introduction and the trapping alternative should be supported by at least a toy-model demonstration that the post-tunnelling field configuration is far enough from the true vacuum to inflate.

Minor objections (11)

[Sec. 2.4, Eq. (2.25)] As printed, Eq. (2.25) does not follow from Eq. (2.24): the left side carries |2λbare|^{1/2} where dimensional analysis requires |2λbare|^{J/2}. Eq. (2.26) is consistent with Eq. (2.24), so this appears to be a typographical slip in the intermediate equation; please check.
[Sec. 2.3] The text states dλ/dn = 2ne²/Z, but Eqs. (2.5) and (2.9) give dλ/dn = ne²/Z, and the final inequality (2.19) appears to use the latter. Please reconcile the factor of two.
[Sec. 2.5] The sentence 'this reduces q_i^{1/2}, but only by √2' omits the intermediate step: D = 2^J reduces the required q_i by a factor of 2, hence q_i^{1/2} by √2. Please spell this out.
[Sec. 3.4, Eqs. (3.15) and (3.18)] Evaluating Eq. (3.15) at n_j = 1 gives 27π²M_Pl⁴/q², whereas Eq. (3.18) gives 432π²M_Pl⁴/q², a factor of 16 larger. The text says the n_j = 1 case receives 'additional suppression due to gravity,' but the numerical factor moves in the opposite direction. Please state whether Eq. (3.18) includes a gravitational correction and, if so, its sign and derivation.
[Sec. 2.4, Eq. (2.26)] Eq. (2.26) gives a typical spacing, not a bound on the probability that the shell is empty. A short Poisson-type estimate of that probability would convert the heuristic volume argument into a quantitative statement and would also make the role of D more transparent.
[Sec. 2.6, Eq. (2.44)] The passage from Eq. (2.41) to Eq. (2.44) is not shown, and the numerical prefactors (the 2^{-1/2} and the π in ω/πD) are not derived. Please include the intermediate steps, and likewise for Eq. (3.10).
[Fig. 1 and caption] The caption should state explicitly that the shell has thickness Δr given by Eq. (2.23) and that the figure is drawn for J = 2, so that the reader does not mistake the circle for the J-dimensional case.
[Sec. 3.3] The selection argument assumes a volume or observer weighting that is never specified, even though the scenario produces an eternally inflating multiverse in which the measure is nontrivial. A sentence acknowledging that the weighting is assumed rather than derived would be appropriate.
[Sec. 3.2.1] The claim that density perturbations can be produced rests on the standard slow-roll spectrum; the paper does not compute an amplitude or spectral index, and it would be clearer to say that the standard inflationary result is assumed rather than derived here.
[Sec. 4 and Sec. 1] Several typographical errors should be corrected: 'sourcs' in Sec. 1, 'as assumed' for 'was assumed' in Sec. 2.2, and 'tunnellling' in Sec. 3.2.3.
[Sec. 4, Ref. [50]] Ref. [50] is cited for the statement that naked-singularity parameters are discrete and can change across a domain wall; a more precise pointer to the relevant section or equation of that work would help the reader verify the analogy.

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The paper

The paper claims

The paper argues that four-form flux is quantized, so the cosmological constant takes only discrete values, and that with enough independent fluxes those values become dense enough to include the observed one.

The reading

The paper asks whether the cosmological constant can be a dynamical variable that settles to a small value on its own, rather than a fixed number that must be cancelled by symmetry. Its first move is to argue that the field strength of a four-form gauge field, usually treated as a continuous constant, is quantized, so the vacuum energy it contributes comes in discrete steps. One flux gives steps far too coarse to land in the observed window, but with many independent fluxes the allowed energies form a fine grid, a 'discretuum', and the authors estimate how many fluxes are needed. The second move is cosmological: membranes nucleate in de Sitter space and lower the flux one unit at a time, so regions with every allowed vacuum energy get produced, including ones in the range where galaxies can form. If right, a small nonzero cosmological constant is not a fine-tuning but a selection effect among exponentially many regions.

What carries the argument

The load-bearing object is the discretuum: the set of allowed vacuum energies $lambda = lambda_{bare} + frac{1}{2}sum_{i=1}^{J} n_i^2 q_i^2$, viewed as the squared radii of integer lattice points in $J$ dimensions with spacings $q_i$. Cancellation of a negative bare cosmological constant becomes a geometric question, whether a shell of radius $sqrt{2|lambda_{bare}|}$ and width $Delta r = |2lambda_{bare}|^{-1/2}Delta lambda$ contains a lattice point, and the answer gives the level spacing in Eq. (2.26). What makes the grid fine enough is the generalized Dirac quantization condition applied to the dual zero-form, $F_0 = en/Z$, which fixes the $q_i$ in terms of membrane charges and compactification volumes. The second piece of machinery is the Brown-Teitelboim dynamics: membrane nucleation moves the integers $n_i$ down by one, so the cosmology is a random walk on the same grid, and de Sitter thermal fluctuations supply the inflaton displacement needed for reheating.

Extended reading notes

Core claim

The central claim is that four-form flux is quantized not only in the sense that its integral over a closed four-manifold is an integer multiple of $2/e$, but that the flux itself takes discrete values $c = en/Z$ with $n$ an integer. The authors argue this from the dual zero-form: when a theory has both electric and magnetic sources, the dual field strength evaluated at a point must be quantized, and in an M-theory compactification on a seven-manifold this follows from the M5-brane charge condition. The immediate consequence is bad for the old idea that a single flux cancels the bare cosmological constant, because the spacing is enormous compared with $10^{-120}M_{Pl}^4$. The rescue is multiplicity. With $J$ independent fluxes the vacuum energy is $lambda = lambda_{bare} + frac{1}{2}sum_i n_i^2 q_i^2$, so the allowed values are squared radii of points on a $J$-dimensional grid; if the charges are incommensurate, a thin shell of radius $sqrt{2|lambda_{bare}|}$ and width set by the observational bound will contain a grid point. The authors estimate that of order 100 fluxes suffice at the GUT or Planck scale, while four or five suffice if the fundamental scale is near a TeV with large extra dimensions. They then extend the Brown-Teitelboim membrane-nucleation cosmology to many fluxes: starting from generic initial conditions with positive vacuum energy, repeated nucleation is a random walk on the grid that populates every point with $lambda > 0$, so regions with $lambda$ in the Weinberg window exist and expand eternally. They further argue that the Gibbons-Hawking temperature of the pre-final de Sitter phase can keep an inflaton field randomly displaced until the final nucleation, after which it rolls and reheats, addressing the empty-universe problem.

Load-bearing premise

The whole density estimate assumes the membrane charges are frozen, incommensurate constants; the authors explicitly set the moduli problem aside and work in an artificial model with fixed charges, so if the compactification volume and background moduli are not stabilized independently of the fluxes, the flux energy is a potential for those moduli rather than a fixed grid.

Editorial extensions

If this is right

The cosmological constant becomes a discrete label of a vacuum rather than a continuous parameter, so exact zero is not special and a small nonzero value is generic.
The spectrum of allowed vacuum energies is computable from the charges of the compactification's three-cycles, giving a concrete target for model building in M theory.
Decay rates out of a small-$lambda$ phase are estimated to be negligible, so the selected vacuum survives long enough to host structure.
In large-extra-dimension scenarios the same fluxes that make membrane charges small tie the hierarchy problem and the cosmological constant problem to a single problem: stabilizing large radii.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the discretuum is real, the number of vacua with $lambda$ in the observational window grows with the number of three-cycles, which points toward a statistical prediction for the distribution of $lambda$ rather than a unique value.
The mechanism predicts that any residual cosmological constant is nonzero and set by the nearest grid point, so a measured $Lambda$ near the window is consistent with the picture but not sharply predicted by it.
The natural follow-up is a compactification in which the fluxes both stabilize the moduli and supply the discretuum; that would turn the density estimate from a plausibility argument into a computation.
Because the same nucleation random walk populates every flux configuration, other flux-dependent couplings may also be selected environmentally, not just the vacuum energy.

Original abstract

A four-form gauge flux makes a variable contribution to the cosmological constant. This has often been assumed to take continuous values, but we argue that it has a generalized Dirac quantization condition. For a single flux the steps are much larger than the observational limit, but we show that with multiple fluxes the allowed values can form a sufficiently dense `discretuum'. Multiple fluxes generally arise in M theory compactifications on manifolds with non-trivial three-cycles. In theories with large extra dimensions a few four-forms suffice; otherwise of order 100 are needed. Starting from generic initial conditions, the repeated nucleation of membranes dynamically generates regions with a cosmological constant in the observational range. Entropy and density perturbations can be produced.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,436 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.66 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.88 · compares with prior results 0.38 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

A four-form gauge flux makes a variable contribution to the cosmological constant. This has often been assumed to take continuous values, but we argue that it has a generalized Dirac quantization condition. For a single flux the steps are much larger than the observational limit, but we show that with multiple fluxes the allowed values can form a sufficiently dense `discretuum'. Multiple fluxes generally arise in M theory compactifications on manifolds with non-trivial three-cycles. In theories with large extra dimensions a few four-forms suffice; otherwise of order 100 are needed. Starting from generic initial conditions, the repeated nucleation of membranes dynamically generates regions with a cosmological constant in the observational range. Entropy and density perturbations can be produced.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A four-form gauge flux makes a variable contribution to the cosmological constant.	background 1.00	0.12	0.05	asserted 1.00
s1	This has often been assumed to take continuous values, but we argue that it has a generalized Dirac quantization condition.	contribution 0.56	0.51	0.33	asserted 0.60
s2	For a single flux the steps are much larger than the observational limit, but we show that with multiple fluxes the allowed values can form a sufficiently dense `discretuum'.	result 0.83	0.89	0.31	asserted 0.99
s3	Multiple fluxes generally arise in M theory compactifications on manifolds with non-trivial three-cycles.	background 0.94	0.15	0.03	asserted 0.96
s4	In theories with large extra dimensions a few four-forms suffice; otherwise of order 100 are needed.	result 0.84	0.63	0.06	asserted 0.97
s5	Starting from generic initial conditions, the repeated nucleation of membranes dynamically generates regions with a cosmological constant in the observational range.	result 0.74	0.79	0.52	asserted 0.99
s6	Entropy and density perturbations can be produced.	result 0.88	0.55	0.05	hedged possibility 0.72

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from argument 0.76.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** The allowed values of the four-form energy density are given by the radius-squared of points in the grid, whose dimension is the number of four-forms J. The spacing in direction i is qi . The negative of the bare cosmological constant corresponds to a (J − 1)-dimensional sphere, and cancellation is possible if there is at least one grid point sufficiently close to the sphere. An important feature of this result is that that the qi need not be exceedingly small if there are more than two four-form fields. In order to achieve a small λ, it is sufficient that there be a discrepancy…

Figures reproduced from arXiv:hep-th/0004134 by the authors.

References

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hep-th 2003-08 accept novelty 8.0 of 10

A warped throat produces a flat brane-antibrane inflaton potential, but superpotential stabilization of the compactification volume generically gives the inflaton m^2 = 2H^2 and ends slow roll.
Counting Flux Vacua
hep-th 2003-07 accept novelty 8.0 of 10

The expected number of supersymmetric flux vacua in type IIb Calabi-Yau compactification is given by a curvature integral over moduli space, growing as (2 pi L)^K / K! in the total flux L.

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hep-th 2001-12 conditional novelty 8.0 of 10

Anti-D3 branes in the Klebanov-Strassler geometry form a classically stable fivebrane that quantum-mechanically tunnels to a supersymmetric vacuum with one less unit of flux, at an exponentially suppressed rate.
Catastrophic Inflation in the Axiverse
hep-th 2026-08 conditional novelty 7.0 of 10

String-theory axions in explicit Calabi-Yau compactifications can produce small-field slow-roll inflation via volume-tuned catastrophes, though no example yet matches both the observed tilt and amplitude of density pe...
The Lorentzian Geometry of Tunneling in Global de Sitter at Late Time
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A late-time Lorentzian Hamiltonian/WKB calculation of bubble nucleation in de Sitter reproduces the CDL decay exponent for all tunneling types, with gravity-dominated bubbles going on-shell at the parent horizon.
Dark Energy and Neutrino Flavor from the Weak Axion
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The dark-energy scale is predicted from neutrino masses and PMNS mixing: the weak-axion Coleman-Weinberg potential lands at 1-4 meV for current neutrino data.
dS$^4$ Metamorphosis
hep-th 2026-02 conditional novelty 7.0 of 10

Higher spin gravity path integral on S^4 glues to an Sp(N) or superconformal S^3 boundary theory, giving leading contribution 2^N with one-loop cancellations.
Boiling After the Dust Settles: Constraining First-Order Phase Transitions During Dark Energy Domination
hep-ph 2025-09 conditional novelty 7.0 of 10

CMB anisotropies from stochastic bubble nucleation constrain late-time phase transitions to release less than ~1% of dark energy when β/H⋆≲25, much tighter than Hubble-budget limits.
$\Lambda_{\rm s}$CDM cosmology from a type-II minimally modified gravity
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Λ_s VCDM is a predictive model combining Λ_s CDM with VCDM gravity via an auxiliary scalar field and sigmoid-smoothed potentials to enable stable mirror AdS-to-dS transitions with possible transient acceleration.
Relaxion Monodromy and the Weak Gravity Conjecture
hep-th 2015-11 conditional novelty 7.0 of 10

Coupling the relaxion to a 3-form field makes its potential consistent with the axion's discrete gauge symmetry, and the Weak Gravity Conjecture then caps the cutoff of such models near 10^9 GeV.
Universality Class in Conformal Inflation
hep-th 2013-06 conditional novelty 7.0 of 10

Any conformally invariant two-field model whose potential depends only on the ratio of the two scalars predicts the same leading-order CMB tilt and tensor fraction, because the frame change stretches the field range e...
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hep-th 2011-12 conditional novelty 7.0 of 10

Random-matrix analysis of the Hessian in N=1 supergravity with many fields shows that the fraction of de Sitter critical points that are metastable falls as exp(-c N^p), with p near 1.3 to 1.5.
String Axiverse
hep-th 2009-05 unverdicted novelty 7.0 of 10

String theory predicts an axiverse of ultralight axions whose effects on CMB polarization, matter power spectrum, and black hole superradiance can be probed by future astrophysical experiments.
Landscape of superconducting membranes
hep-th 2009-01 accept novelty 7.0 of 10

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hep-th 2005-07 conditional novelty 7.0 of 10

A ten-dimensional formula for the potential of warped flux compactifications is derived, yielding a slope-dominance criterion for de Sitter vacua and a warping-corrected definition of holomorphic Kahler moduli.
Fluxes, moduli fixing and MSSM-like vacua in a simple IIA orientifold
hep-th 2005-06 conditional novelty 7.0 of 10

Adding RR, NS and metric fluxes to a T^6/(Omega(-1)^F_L I_3) Type IIA orientifold stabilizes all closed-string moduli in supersymmetric AdS vacua, and one such vacuum hosts a three-generation MSSM-like intersecting D6...
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hep-th 2004-11 accept novelty 7.0 of 10

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Landscape, the Scale of SUSY Breaking, and Inflation
hep-th 2004-11 conditional novelty 7.0 of 10

In the simplest KKLT model the inflationary Hubble scale is bounded by the gravitino mass, but a racetrack superpotential with a supersymmetric Minkowski minimum decouples the two scales.
Aspects of Split Supersymmetry
hep-ph 2004-09 accept novelty 7.0 of 10

Split Supersymmetry's heavy-scalar, light-fermion spectrum can emerge naturally from R-symmetric supersymmetry breaking, and it predicts electric dipole moments near current limits plus a gravitino-boosted dark matter...
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hep-th 2004-04 accept novelty 7.0 of 10

Flux vacua in IIb Calabi-Yau compactification follow a computable density built from special geometry, strongly enhanced near conifold points, with a cosmological constant distribution that is uniform near zero.
Scalar Speed Limits and Cosmology: Acceleration from D-cceleration
hep-th 2003-10 conditional novelty 7.0 of 10

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Infrared Screening of the Cosmological Constant
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The authors construct a massive propagating scalar for coupling constants via a defect-based kinetic term that preserves conserved charges and original black hole solutions on constant-coupling configurations.
Calabi-Yau Orientifold Hypersurfaces and their F-theory Uplifts
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An algorithm builds Calabi-Yau orientifolds and F-theory fourfold uplifts from 6d reflexive polytopes derived from orientifold data, with code in CYTools and GitHub.
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Axiverse Lampposts
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In a hierarchical multi-axion theory with random couplings, axion field ranges shrink with 1/sqrt(N), generic axion–SM couplings are suppressed, but the QCD axion's coupling is unsuppressed.
Microstate counting from defects in de Sitter
hep-th 2025-11 conditional novelty 6.0 of 10

Counting defect microstates via Lorentzian wormholes reproduces the de Sitter and Schwarzschild-de Sitter entropy area laws.
Emergent Dark Matter
hep-ph 2025-11 conditional novelty 6.0 of 10

Dark matter is modeled as the emergent massive in-medium state of a 3-form gauge field that otherwise behaves as dark energy.
O(16)$\times$O(16) heterotic theory on $AdS_3\times S^3\times T^4$
hep-th 2025-10 conditional novelty 6.0 of 10

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hep-th 2025-09 conditional novelty 6.0 of 10

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hep-th 2025-06 conditional novelty 6.0 of 10

A conditional variational autoencoder trained on known Type IIB flux vacua can generate new physically valid flux vectors with targeted superpotential values faster than Metropolis sampling.
Nonperturbative Quantum Gravity in a Closed Lorentzian Universe
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hep-th 2025-01 conditional novelty 6.0 of 10

An enumeration algorithm for Type IIB flux vacua yields millions of explicit vacua in a two-modulus Calabi-Yau, exposing deviations from statistical predictions and a vacuum with |W0| about 5.5 x 10^-5.
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hep-ph 2024-12 conditional novelty 6.0 of 10

Detection of an isolated SU(2)_L n-plet with n≥5 would falsify known string constructions; current LHC limits exclude such states up to 400-735 GeV depending on n.
Holography and the KKLT Scenario
hep-th 2022-04 conditional novelty 6.0 of 10

A holographic bound on the central charge of the dual conformal field theory forces the KKLT anti-de Sitter vacuum to sit at or below the species scale, so the effective field theory used to construct it is invalid.
A Cosmological Constant That is Too Small
hep-th 2021-07 conditional novelty 6.0 of 10

A type IIB flux compactification on an orientifold of a Calabi-Yau threefold yields a supersymmetric AdS4 vacuum with vacuum energy about 10^-144 Planck units and Kaluza-Klein radius about 10^4 Planck lengths.
Small Cosmological Constants in String Theory
hep-th 2021-07 conditional novelty 6.0 of 10

Explicit type IIB orientifolds with quantized fluxes admit supersymmetric AdS4 vacua in which all closed-string moduli are stabilized and the cosmological constant is below 10^-123 in Planck units.
The FL bound and its phenomenological implications
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hep-th 2020-06 conditional novelty 6.0 of 10

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Eternal Inflation in Swampy Landscapes
gr-qc 2019-08 conditional novelty 6.0 of 10

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hep-ph 2019-08 accept novelty 6.0 of 10

A shallow local minimum added to a hilltop inflation potential can make the typical number of e-folds as large as 10^(10^10), enough for light scalars to reach Bunch-Davies equilibrium.
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hep-th 2019-08 conditional novelty 6.0 of 10

Gaugino condensation on D7-branes plus anti-D3-branes produce a ten-dimensional stress-energy that exactly reproduces the KKLT four-dimensional scalar potential and curvature.
F-theory and Dark Energy
hep-th 2018-11 conditional novelty 6.0 of 10

F-theory on a warped Spin(7) times fluxed S^3 background is argued to give a 4D vacuum with cancelled zero-point energy and superpartner masses split by the geometric mean of the IR and UV cutoffs.
Emergent de Sitter Cosmology from Decaying AdS
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A New Semiclassical Picture of Vacuum Decay
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Classical evolution of sampled vacuum fluctuations reproduces bubble nucleation and the instanton decay rate in a 1+1D scalar field theory, suggesting vacuum decay need not involve tunneling.
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Machine Learning in the String Landscape
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gr-qc 2016-10 conditional novelty 6.0 of 10

Multiple shooting with analytic end regions and an auxiliary translation variable solves multi-field vacuum-decay bounce equations, reaching eight fields in about an hour, with a released Mathematica package.
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hep-th 2015-11 conditional novelty 6.0 of 10

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Minkowski 3-forms, Flux String Vacua, Axion Stability and Naturalness
hep-th 2015-07 conditional novelty 6.0 of 10

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hep-th 2015-07 conditional novelty 6.0 of 10

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See all 162 Pith citations

How later papers used it

443 later papers cite it

Evidence: substantial. 425 of the citing papers share no author with it, and 30 of those carry a confident label from Pith's citation classifier.

Pith read 39 of the 688 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 1 built on it and 1 compared its own results with it.

Builds on it 1 of 6 papers with this label

Here we show how it is generalised to a much wider class of models which could, in principle, include the Bousso-Polchinski set-up [ref] .

The cosmological constant is probably still zero (2023) · Nucleation rates · 0.97

Compares with it 1 of 11 papers with this label

Compared its own scenarios, which rely on a single four-form flux of electroweak scale to get both the Higgs mass and the cosmological constant at right scales, with this paper's proposal where multiple four-form fluxes were introduced for scanning the cosmological constant with the precision of the observed value.

The Selfish Higgs and Reheating (2019) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

420 arXiv papers cite this in 641 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 409 sentences without a confident label

Contests it 1 paper

However the analysis in [ref] does not take moduli stabilization into account and the resultant distribution of quantized fluxes does not imply the preference of a small cosmological constant.

Probability of Vacuum Stability in Type IIB Multi-K\"ahler Moduli Models · Introduction · contest 0.84

Builds on it 6 papers

What we try to do in the next section is to modify this latter mechanism by including a larger number $J$ of different four-forms in order to avoid the gap problem, in the same spirit of the BP extension of the BT mechanism [ref] .

Environmental selection of the cosmological constant and electroweak scales · Four-forms and environmental selection of the electroweak scale · 0.94
Here we show how it is generalised to a much wider class of models which could, in principle, include the Bousso-Polchinski set-up [ref] .

The cosmological constant is probably still zero · Nucleation rates · 0.97
In its simplest incarnation, our approach is a generalization of the idea pioneered in [ref] about discharging cosmological constant by nonperturbative membrane nucleation processes, and also benefits from results of [ref] .

Implications of Weak Gravity Conjecture for de Sitter Decay by Flux Discharge · Introduction · 0.96

Uses its data or values 5 papers

If current estimates of the number of vacua [ref] hold up, i.e., if $log_10 N$ is of order hundreds,[The number of anthropic vacua, $N̅$, may be smaller by dozens or even hundreds of orders of magnitude than the total number of vacua, $N$, for low-energy reasons that are unrelated to the cosmological constant or curvature and so are not included in out analysis.

Geometric origin of coincidences and hierarchies in the landscape · Positive cosmological constant · 0.85
The number of flux vacua on a given CY background space is very huge [ref] : $N_vac∼10^500$.

String Landscape and the Standard Model of Particle Physics · Moduli stabilization · 0.92
For example, a typical of tunneling probability (using the thin wall Coleman-De Luccia result) in the Bousso-Polchinski scenario is $∼e^-100$ [ref] .

Rapid Tunneling and Percolation in the Landscape · Percolation in the Landscape: Efficient Tunneling and Preferred Paths · 0.91

Compares with it 9 papers

Note that for the benchmark point of $J=100$ of [ref] we find that $q_GL ≈q_BP/2$ and indication that a simultaneous solution to the CC and EW hierarchy problems can be found in the presence of a mild hierarchy between $v$ and $Λ^1/4$ at the expense of introducing a weak coupling between the four-forms and the Higgs scalar.

Environmental selection of the cosmological constant and electroweak scales · Arbitrary J · 0.98
This is a significant departure from the anthropic arguments usually presented for the Bousso-Polchinski set-up [ref] .

The cosmological constant is probably still zero · The Bousso-Polchinski set-up · 0.83
However there are important technical differences when we compare to those models since in our theory the bulk cosmological constant depends on the $4$-form dual magnetic fluxes (bi)linearly, as opposed to quadratically [ref] , as is clear from Eq. ([ref]).

Pancosmic Relativity and Nature's Hierarchies · Lg · 0.99

Cites it as support 10 papers

This has three important consequences: * Individual pocket universes, including ours, can have very long lifetimes easily exceeding 10 Gyr [ref] . * When a bubble of new vacuum does form, it will be highly symmetric [ref] .

The Cosmological Constant Problem, Dark Energy, and the Landscape of String Theory · Connecting with Standard Cosmology · 0.96
However, as emphasized in [ref] the actual value of the 4-form field strength in four dimensions (and not only its shift when crossing a membrane) satisfies Dirac quantization.

Relaxion Monodromy and the Weak Gravity Conjecture · Axion monodromy · 0.97
So the cosmological constant does not always dominate, but just sometimes [ref] .

Hidden Variables of Gravity and Geometry and the Cosmological Constant Problem · Introduction · 0.96

Cites it as background 180 papers

Under flux compactifications [ref] , an enormous number of different compactification possibilities are available [ref] , each leading to different 4-d laws of physics.

Fine-tuned vs. natural supersymmetry: what does the string landscape predict? · Introduction · 0.91
Advances in String Theory over the last five years led to the discovery of the landscape of string theory [ref] .

Birth of the Universe from the Multiverse · String Landscape Multiverse · 0.95
Consider multiverse theories (such as what one might expect from a string/M theory landscape [ref] ) in which the quantum state gives a superposition of different possible `constants' of physics.

Statistical Evidence Against Simple Forms of Wavefunction Collapse · Introduction · 0.94

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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