The open string Veneziano amplitude emerges as the unique tree-level completion of N=4 super Yang-Mills when supersymmetry, factorization, and positivity are imposed.
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On the Geometry of the String Landscape and the Swampland
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abstract
We make a number of conjectures about the geometry of continuous moduli parameterizing the string landscape. In particular we conjecture that such moduli are always given by expectation value of scalar fields and that moduli spaces with finite non-zero diameter belong to the swampland. We also conjecture that points at infinity in a moduli space correspond to points where an infinite tower of massless states appear, and that near these regions the moduli space is negatively curved. We also propose that there is no non-trivial 1-cycle of minimum length in the moduli space. This leads in particular to the prediction of the existence of a radially massive partner to the axion. These conjectures put strong constraints on inflaton potentials that can appear in a consistent quantum theory of gravity. Our conjectures are supported by a number of highly non-trivial examples from string theory. Moreover it is shown that these conditions can be violated if gravity is decoupled.
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The Schwinger integral over light towers captures precisely the instantons with actions in the window (Λ_sp/M_light)^{-1} ≤ S_inst ≤ Λ_sp/M_light, as verified in eight- and seven-dimensional toroidal compactifications.
In codimension-one warped compactifications with exponential potentials, the KK mass decay rate λ_KK is reduced by warping but still satisfies the Sharpened Distance Conjecture precisely when the higher-dimensional potential obeys the Strong de Sitter condition.
All integrable 2D Horndeski theories (and thus many regular black-hole metrics) arise as spherical reductions of pure d≥4 gravities, which the paper terms quasi-topological.
RG-improved black hole spacetimes with scale-dependent gravitational coupling are derived as vacuum solutions to 2D Horndeski master field equations, embedding prior works and exposing implementation discrepancies.
In N=2 SU quiver theories the large-N Hagedorn temperature depends only on quiver length for linear cases and equals that of N=4 SYM for holographic quivers, with a universal lower bound of 1/sqrt(2) on the exponential rate alpha of higher-spin current conservation.
Explicit scale-separated dS5 maximum in M-theory on a 6D Riemann-flat manifold with vacuum energy 10^{-8} in Planck units, obtained via Casimir energies and fluxes.
Sharpened Dynamical Cobordism ties the allowed range of critical exponent δ to theory structure ξ, flagging obstructions from non-trivial cobordism charges that require new degrees of freedom.
Wormhole solutions with imaginary scalars set an Imaginary Distance Bound on analytic continuation of couplings, enforced by stringy effects that coincide with WGC and KSW in special cases.
Positivity of gravitational path integral inner products requires non-perturbative instabilities in axion wormholes that break shift symmetry, implying a sharp axion weak gravity conjecture with precise constants.
Optimal transport yields a generalized Wasserstein distance on field space, obtained from a WKB expansion of a Schrödinger equation and extended to dynamical gravity via the Wheeler-DeWitt equation in the ADM formalism.
Imaginary wormholes and the IDB imply that towers of BPS EFT instantons generate infinitely many superpotential terms that break non-invertible axion shift symmetries in N=1 axiverse models.
The paper defines cones C_BPS-B and C_BPS-BB for BPS branes in supergravity and conjectures that states in C_BPS-BB are realized as BPS states with C_BPS-B as their electric-magnetic dual when moduli-independent.
Using weight polytopes of irreducible representations, a finite list of symmetric moduli spaces satisfies the SDC decay rates; most embed from an E8(8) EFT but three cannot be obtained from string or M-theory compactifications.
Proposes a refinement of the Swampland Cobordism Conjecture for duality groups, arguing that diverging commutator widths necessitate infinitely many duality defects to realize monodromies in 9d supergravity bordisms.
Proposes phase-resolved invariant path-length criteria and a master formula for lower bound on ε_ek in ekpyrotic cosmologies, using BKL suppression and conversion windows as constraints.
Exact infrared solutions for surface criticalities in the Gross-Neveu-Yukawa model encode fermionic anomalies in surface dynamics and reveal emergent structures linked to a defect version of the CFT distance conjecture.
Non-perturbative g_s corrections obstruct perturbative Type IIB descriptions and can remove classical infinite distance degenerations in asymptotic regions of the complex structure moduli space.
Five-dimensional rotating primordial black holes with initial masses above 10^10 grams survive to today and can account for all dark matter due to suppressed Hawking radiation and memory burden effects in the micron-scale dark dimension.
In asymptotically safe gravity, dimension-five couplings of ultralight scalar dark matter to gauge field strengths vanish and are not generated perturbatively.
Quintessence models satisfying NEC everywhere predict the w0 > -1 and w0+wa < -1 sector favored by data, due to an approximate degeneracy in the w(z) = w0 + wa z/(1+z) parameterization.
A supergravity construction using two chiral superfields embeds arbitrary F(R) gravity as a UV completion of Starobinsky inflation, stabilized by the dilaton and consistent with swampland constraints in a heterotic string example.
Quantum corrections obstruct infinite distance limits in Type IIA orientifold Kähler moduli unless other moduli are also taken to infinity, as shown by worldsheet EFT strings, massless towers, and M-theory G2 uplifts.
SWIM solves Warm Inflation stochastic perturbations fully numerically, speeds MCMC with machine learning, and integrates with Cobaya to constrain any Warm Inflation model against CMB data.
citing papers explorer
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String Theory from Maximal Supersymmetry
The open string Veneziano amplitude emerges as the unique tree-level completion of N=4 super Yang-Mills when supersymmetry, factorization, and positivity are imposed.
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Taxonomy of Instanton Corrections in Infinite Distance Limits
The Schwinger integral over light towers captures precisely the instantons with actions in the window (Λ_sp/M_light)^{-1} ≤ S_inst ≤ Λ_sp/M_light, as verified in eight- and seven-dimensional toroidal compactifications.
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Alice in Warpland: KK modes, Warped Compactifications and the Swampland
In codimension-one warped compactifications with exponential potentials, the KK mass decay rate λ_KK is reduced by warping but still satisfies the Sharpened Distance Conjecture precisely when the higher-dimensional potential obeys the Strong de Sitter condition.
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All $2D$ generalised dilaton theories from $d\geq 4$ gravities
All integrable 2D Horndeski theories (and thus many regular black-hole metrics) arise as spherical reductions of pure d≥4 gravities, which the paper terms quasi-topological.
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Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry
RG-improved black hole spacetimes with scale-dependent gravitational coupling are derived as vacuum solutions to 2D Horndeski master field equations, embedding prior works and exposing implementation discrepancies.
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The CFT Distance Conjecture and Tensionless String Limits in $\mathcal N=2$ Quiver Gauge Theories
In N=2 SU quiver theories the large-N Hagedorn temperature depends only on quiver length for linear cases and equals that of N=4 SYM for holographic quivers, with a universal lower bound of 1/sqrt(2) on the exponential rate alpha of higher-spin current conservation.
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An M-theory dS maximum from Casimir energies on Riemann-flat manifolds
Explicit scale-separated dS5 maximum in M-theory on a 6D Riemann-flat manifold with vacuum energy 10^{-8} in Planck units, obtained via Casimir energies and fluxes.
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Sharpened Dynamical Cobordism
Sharpened Dynamical Cobordism ties the allowed range of critical exponent δ to theory structure ξ, flagging obstructions from non-trivial cobordism charges that require new degrees of freedom.
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Wormholes and the imaginary distance bound
Wormhole solutions with imaginary scalars set an Imaginary Distance Bound on analytic continuation of couplings, enforced by stringy effects that coincide with WGC and KSW in special cases.
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Positivity of the gravitational path integral implies the axionic weak gravity conjecture
Positivity of gravitational path integral inner products requires non-perturbative instabilities in axion wormholes that break shift symmetry, implying a sharp axion weak gravity conjecture with precise constants.
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Optimal paths across potentials on scalar field space
Optimal transport yields a generalized Wasserstein distance on field space, obtained from a WKB expansion of a Schrödinger equation and extended to dynamical gravity via the Wheeler-DeWitt equation in the ADM formalism.
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Non-invertible symmetries in the axiverse, and the imaginary wormholes
Imaginary wormholes and the IDB imply that towers of BPS EFT instantons generate infinitely many superpotential terms that break non-invertible axion shift symmetries in N=1 axiverse models.
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On BPS Branes
The paper defines cones C_BPS-B and C_BPS-BB for BPS branes in supergravity and conjectures that states in C_BPS-BB are realized as BPS states with C_BPS-B as their electric-magnetic dual when moduli-independent.
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EFTs with Symmetric Moduli Spaces: the Landscape and the Swampland
Using weight polytopes of irreducible representations, a finite list of symmetric moduli spaces satisfies the SDC decay rates; most embed from an E8(8) EFT but three cannot be obtained from string or M-theory compactifications.
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Bordisms between 9d type IIB supergravities and commutator widths of duality groups
Proposes a refinement of the Swampland Cobordism Conjecture for duality groups, arguing that diverging commutator widths necessitate infinitely many duality defects to realize monodromies in 9d supergravity bordisms.
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Phase-resolved field-space distance criteria in ekpyrotic, bouncing and cyclic cosmologies
Proposes phase-resolved invariant path-length criteria and a master formula for lower bound on ε_ek in ekpyrotic cosmologies, using BKL suppression and conversion windows as constraints.
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Extraordinary Surface Criticalities for Interacting Fermions
Exact infrared solutions for surface criticalities in the Gross-Neveu-Yukawa model encode fermionic anomalies in surface dynamics and reveal emergent structures linked to a defect version of the CFT distance conjecture.
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Quantum obstructions for $N=1$ infinite distance limits -- Part I: $g_s$ obstructions
Non-perturbative g_s corrections obstruct perturbative Type IIB descriptions and can remove classical infinite distance degenerations in asymptotic regions of the complex structure moduli space.
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5D Rotating Black Holes as dark matter in Dark Dimension Scenario: Hawking Radiation versus the Memory Burden Effect
Five-dimensional rotating primordial black holes with initial masses above 10^10 grams survive to today and can account for all dark matter due to suppressed Hawking radiation and memory burden effects in the micron-scale dark dimension.
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Towards theory constraints on ultralight dark matter from quantum gravity
In asymptotically safe gravity, dimension-five couplings of ultralight scalar dark matter to gauge field strengths vanish and are not generated perturbatively.
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Assessing observational constraints on dark energy
Quintessence models satisfying NEC everywhere predict the w0 > -1 and w0+wa < -1 sector favored by data, due to an approximate degeneracy in the w(z) = w0 + wa z/(1+z) parameterization.
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Ultraviolet completion of Starobinsky inflation
A supergravity construction using two chiral superfields embeds arbitrary F(R) gravity as a UV completion of Starobinsky inflation, stabilized by the dilaton and consistent with swampland constraints in a heterotic string example.
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On Quantum Obstructions in Type IIA Orientifolds
Quantum corrections obstruct infinite distance limits in Type IIA orientifold Kähler moduli unless other moduli are also taken to infinity, as shown by worldsheet EFT strings, massless towers, and M-theory G2 uplifts.
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SWIM: Stochastic Warm Inflation Module to generate and analyse Warm Inflationary power spectrum
SWIM solves Warm Inflation stochastic perturbations fully numerically, speeds MCMC with machine learning, and integrates with Cobaya to constrain any Warm Inflation model against CMB data.
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Sampling the Graviton Pole and Deprojecting the Swampland
A sampling-based bootstrap for graviton poles in EFTs yields non-projective bounds that fix the EFT cutoff scale relative to the Planck mass, with M/M_P ≲ 7.8 in D=5.
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A Circle That Won't Return: The Fate of RR Fluxes and D-branes in Type 0A Tachyon Condensation
In type 0A on a two-circle wedge, isolated collapsing-branch D_p^- sources incur infinite RR field energy cost as the branch shrinks, with possible infrared screening or discharge to D_p^+ via an effective relative-charge carrier.
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Quantum Gravity Cutoff from Axions: A Type IIB Landscape Study
The bound Λ_QG ≲ 2π √S f holds for C2 and C4 axions in Type IIB Calabi-Yau compactifications even near Kähler moduli space boundaries where co-scaling fails.
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Moduli Stabilisation for ADD and the Dark Dimension Scenario
A perturbative stabilization mechanism in the Large Volume Scenario for K3-fibered Calabi-Yau threefolds generates exponentially large 2D base volumes while keeping the 4D fibre small, enabling ADD or Dark Dimension limits with possible dS or quintessence vacua.
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Gravity Decoupling and Axionic Shift Symmetries
Axionic string tensions define vector fields on moduli space that split into mutually orthogonal subsets with one decoupling from gravity, and their Laplacian relates to divergent moduli space curvature.
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Sharpening the Supersymmetric Axion Weak Gravity Conjecture
The paper verifies the bound fS/|n| ≤ (π/(2 κ_d)) sqrt((d-1)/(d-2)) for axion instantons and sharpens it to fS/|n| ≤ (1/κ_4) sqrt(7/2) for supersymmetric 4d instantons using three approaches in the string landscape.
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Controlled Penumbral Inflation from Monodromic Valleys
Derives conditions on branch parameters for controlled inflationary plateaus in penumbral monodromic valleys, with an exactly solvable family targeting r ~ 10^{-3} and alpha_s ~ -r/2.
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Searching for a Dark Dimension Right-handed Neutrino in KATRIN
The paper derives KATRIN signatures for a 5D right-handed neutrino and shows that a large part of the compactification scale, bulk mass, and Yukawa coupling parameter space lies within experimental sensitivity, with multiple or single kinks depending on the bulk mass relative to the compactification
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Reviving Motivated Inflationary Potentials with $K$-inflation in the light of ACT
K-inflation with non-canonical kinetic term G(φ) shifts α-attractor T-models and natural inflation into the Planck-ACT-LB-BK18 allowed region while satisfying Swampland conjectures and producing testable GW spectra.
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Some Properties and Uses of the Species Scale
The Species Scale implies Laplace eigenvalue equations for BPS-protected Wilson coefficients and produces a one-loop moduli potential with minima at desert points that may stabilize Kähler moduli in 4d Type IIB orientifolds.
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Imprint of swampland-inspired coupled early dark energy
A swampland-inspired DM-EDE coupling is tested against DESI DR2 BAO data, showing the EDE potential construction affects late-time dark energy constraints.
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Stochastic Survival near Swampland Boundaries
Surviving inflationary histories develop a universal inward drift near any hard swampland boundary — two times the diffusion over the distance to the edge — regardless of the cutoff's microscopic origin.
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Kaleidoscopes, Waves and the Prepotential
Coxeter symmetries from isomorphic flops in Kähler-favorable CICYs make the 4D N=2 prepotential solve the Helmholtz equation on the moduli space, enabling resummed expressions from worldsheet instantons.
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Dark Dimension Right-handed Neutrinos Confronted with Long-Baseline Oscillation Experiments
T2K and NOvA data exclude dark-dimension neutrino models with bulk mass |c| < ~0.1 eV for a 10 µm extra dimension.
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Assisted Fibre Inflation in Perturbative LVS
Multi-field fibre inflation in perturbative LVS uses collective dynamics of several moduli to achieve viable cosmology with sub-Planckian individual field ranges given by total range divided by sqrt(n).
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Induced Multi-phase Inflation with Reheating: Leptogenesis and Dark Matter Production in Metric versus Palatini
Multi-phase non-minimal inflation in metric and Palatini gravity predicts ns between 0.93 and 0.98, r up to 0.03 in metric but below 10^{-5} in Palatini, with non-thermal DM and leptogenesis viable for couplings in the 10^{-7} to 10^{-3} range.
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What to do with a Ricci-flat Calabi--Yau metric?
Numerical Ricci-flat Calabi–Yau metrics turn string compactifications from topological existence statements into computable geometries, unlocking normalized couplings, spectra, and metric-level tests of mirror symmetry.
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Thermal effects and finite-temperature cosmology in perturbatively stabilized large volume scenarios
Examines thermal effects on moduli in perturbatively stabilized LVS, deriving T_max dependence on loop corrections and showing thermal metastability is sensitive to post-inflationary history while favoring high-scale inflation.
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The weak gravity conjecture in perturbative strings
A summary of a proposed proof that the Weak Gravity Conjecture follows from the structure of perturbative bosonic string theory.
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On Thermodynamics of Charged Black Holes, Swampland, and Dark Matter
A thermodynamic treatment of charged black holes is proposed to connect swampland conjectures to the dark dimension and dark matter using dynamical cosmological constant and quasi-static scalar fields.
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Breaking Free from the Swampland of Impossible Universes through the DESI Portal
A review of string-inspired dynamical dark energy models claiming compatibility with DESI's hints of evolving dark energy under swampland constraints.
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Dark energy from string theory: an introductory review
String theory imposes constraints on dark energy but permits various construction attempts for de Sitter vacua and single-field exponential quintessence models despite obstructions.
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In the Realm of the Hubble tension $-$ a Review of Solutions
A review summarizing the Hubble constant tension and proposed solutions from new physics that restore agreement between Planck CMB data and local H0 measurements within 1-2 sigma.
- The Hagedorn Temperature as a Nonequilibrium Dynamical Bottleneck in String Thermodynamics