The paper constructs arbitrary networks of 10d non-tachyonic heterotic string theories via cobordism-implied junctions and gives worldsheet realizations for graphs, higher-dimensional networks, and compact configurations with sectors on different spaces.
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The String Landscape and the Swampland
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abstract
Recent developments in string theory suggest that string theory landscape of vacua is vast. It is natural to ask if this landscape is as vast as allowed by consistent-looking effective field theories. We use universality ideas from string theory to suggest that this is not the case, and that the landscape is surrounded by an even more vast swampland of consistent-looking semiclassical effective field theories, which are actually inconsistent. Identification of the boundary of the landscape is a central question which is at the heart of the meaning of universality properties of consistent quantum gravitational theories. We propose certain finiteness criteria as one relevant factor in identifying this boundary (based on talks given at the Einstein Symposium in Alexandria, at the 2005 Simons Workshop in Mathematics and Physics, and the talk to have been presented at Strings 2005).
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Explicit worldsheet constructions of 9d junctions joining several 10d string theories via generalized RG flow interpolations and closed tachyon condensation, providing dynamical realizations of multi-theory cobordisms.
Non-minimal three-point interactions induce negative one-loop running of Wilson coefficients in gravitational EFTs, yet graviton loops generate positive IR contributions that dominate the bounds after smearing if the species number is bounded.
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.
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.
Supersymmetry, R-symmetry, and positivity constrain planar 4d EFTs to match the open string Veneziano amplitude at tree level.
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.
Defines IR-finite amplitudes M_E that preserve analyticity and unitarity to derive positivity bounds on EFTs including electromagnetism and gravity in D=4.
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.
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.
Derives WGC bounds q/(m r+) ≥ 1/√2 (universal, parameters cancel) in dRGT gravity and q/(m r+) ≥ e^{-γ/2} in ModMax theory from CFT pole analysis, with relaxed forms when assumptions are dropped.
A stochastic survival framework maps swampland control data to conditioned drifts for moduli histories near boundaries via the Doob transform, yielding a universal inward wall response near regular hard boundaries.
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.
Tree-level gravitational scattering under the equivalence principle mandates single-particle states in all irreducible representations constructible from a single seed charge, with equal interaction strengths.
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.
Six-dimensional primordial black holes with memory burden effects can survive as light dark matter in a two-extra-dimension model at the 10 TeV scale, producing high-multiplicity thermal events at future colliders.
Symmetry plus perturbative gravitational scattering consistency requires the abelian charge lattice to be completely populated by single-particle states for SU(N) with N≥3 and SO(N) with N≥5.
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.
Morse-Bott inequalities yield homology bounds and topology-change counts for generic cobordisms to nothing in string theory compactifications.
Derives WGC bound on probe charge-to-mass ratio from positivity of anomalous dimensions in dual CFT for charged particles in higher-derivative AdS black holes, with bound increasing with couplings and ISCOs existing up to the bound.
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.
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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