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  1. A bstract We show that the strong CP problem is solved in a large class of compactifications of string theory. The Peccei-Quinn mechanism solves the strong CP problem if the CP-breaking effects of the ultraviolet completion of gravity and of QCD are small compared to the CP-preserving axion potential generated by low-energy QCD instantons. We characterize both classes of effects. To understand quantum gravitational effects, we consider an ensemble of flux compactifications of type IIB string theory on orientifolds of Calabi-Yau hypersurfaces in the geometric regime, taking a simple model of QCD on D7-branes. We show that the D-brane instanton contribution to the neutron electric dipole moment falls exponentially in N 4 , with N the number of axions. In particular, this contribution is negligible in all models in our ensemble with N > 17. We interpret this result as a consequence of large N effects in the geometry that create hierarchies in instanton actions and also suppress the ultraviolet cutoff. We also compute the CP breaking due to high-energy instantons in QCD. In the absence of vectorlike pairs, we find contributions to the neutron electric dipole moment that are not excluded, but that could be accessible to future experiments if the scale of supersymmetry breaking is sufficiently low. The existence of vectorlike pairs can lead to a larger dipole moment. Finally, we show that a significant fraction of models are allowed by standard cosmological and astrophysical constraints. 
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    Free, publicly-accessible full text available June 1, 2024
  2. A bstract We study Euclidean D3-branes wrapping divisors D in Calabi-Yau orientifold compactifications of type IIB string theory. Witten’s counting of fermion zero modes in terms of the cohomology of the structure sheaf $$ {\mathcal{O}}_D $$ O D applies when D is smooth, but we argue that effective divisors of Calabi-Yau threefolds typically have singularities along rational curves. We generalize the counting of fermion zero modes to such singular divisors, in terms of the cohomology of the structure sheaf $$ {\mathcal{O}}_{\overline{D}} $$ O D ¯ of the normalization $$ \overline{D} $$ D ¯ of D . We establish this by detailing compactifications in which the singularities can be unwound by passing through flop transitions, giving a physical incarnation of the normalization process. Analytically continuing the superpotential through the flops, we find that singular divisors whose normalizations are rigid can contribute to the superpotential: specifically, $$ {h}_{+}^{\bullet}\left({\mathcal{O}}_{\overline{D}}\right)=\left(1,0,0\right) $$ h + • O D ¯ = 1 0 0 and $$ {h}_{-}^{\bullet}\left({\mathcal{O}}_{\overline{D}}\right)=\left(0,0,0\right) $$ h − • O D ¯ = 0 0 0 give a sufficient condition for a contribution. The examples that we present feature infinitely many isomorphic geometric phases, with corresponding infinite-order monodromy groups Γ. We use the action of Γ on effective divisors to determine the exact effective cones, which have infinitely many generators. The resulting nonperturbative superpotentials are Jacobi theta functions, whose modular symmetries suggest the existence of strong-weak coupling dualities involving inversion of divisor volumes. 
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  3. The precision cosmological model describing the origin and expansion history of the universe, with observed structure seeded at the inflationary cosmic horizon, demands completion in the ultraviolet and in the infrared. The dynamics of the cosmic horizon also suggests an associated entropy, again requiring a microphysical theory. Recent years have seen enormous progress in understanding the structure of de Sitter space and inflation in string theory, and of cosmological observables captured by quantum field theory and solvable deformations thereof. The resulting models admit ongoing observational tests through measurements of the cosmic microwave background and large-scale structure, as well as through analyses of theoretical consistency by means of thought experiments. This paper, prepared for the TF01 and TF09 conveners of the Snowmass 2021 process, provides a synopsis of this important area, focusing on ongoing developments and opportunities. Note: Contribution to Snowmass 2021 
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  4. A bstract We construct supersymmetric AdS 4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α ′ expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10 − 123 in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol. 
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    A bstract We develop methods for resummation of instanton lattice series. Using these tools, we investigate the consequences of the Weak Gravity Conjecture for large-field axion inflation. We find that the Sublattice Weak Gravity Conjecture implies a constraint on the volume of the axion fundamental domain. However, we also identify conditions under which alignment and clockwork constructions, and a new variant of N -flation that we devise, can evade this constraint. We conclude that some classes of low-energy effective theories of large-field axion inflation are consistent with the strongest proposed form of the Weak Gravity Conjecture, while others are not. 
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