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We present a complete proof of the Weak Gravity Conjecture in any perturbative bosonic string theory in spacetime dimension D ≥ 6. Our proof works by relating the black hole extremality bound to long range forces, which are more easily calculated on the worldsheet, closing the gaps in partial arguments in the existing literature. We simultaneously establish a strict, sublattice form of the conjecture in the same class of theories. We close by discussing the scope and limitations of our analysis, along with possible extensions including an upcoming generalization of our work to the superstring. 

The Emergent String Conjecture constrains the possible types of light towers in infinite-distance limits in quantum gravity moduli spaces. In this paper, we use these constraints to restrict the geometry of the scalar charge-to-mass vectors -∇ log m of the light towers and the analogous vector -∇ log Λ of the species scale. We derive taxonomic rules that these vectors must satisfy in each duality frame. Under certain assumptions, this allows us to classify the ways in which different duality frames can fit together globally in the moduli space in terms of a finite list of polytopes. Many of these polytopes arise in known string theory compactifications, while others suggest either undiscovered corners of the landscape or new swampland constraints. 

Geodesics in moduli spaces of string vacua are important objects in string phenomenology. In this paper, we highlight a simple condition that connects brane tensions, including particle masses, with geodesics in moduli spaces. Namely, when a brane’s scalar charge-to-tension ratio vector −∇ log T has a fixed length, then the gradient flow induced by the logarithm of the brane’s tension is a geodesic. We show that this condition is satisfied in many examples in the string landscape. 

Axion-like degrees of freedom generally interact with fermions through a shift symmetric coupling. As a consequence, a time-dependent axion will lead to the generation of fermions by amplifying their vacuum fluctuations. We provide the formulae that allow one to determine the spectra of produced fermions in a generic Friedmann-Lemaître-Robertson-Walker Universe with flat spatial slices. Then we derive simple approximate formulae for the spectra of the produced fermions, as a function of the model parameters, in the specific cases of a radiation- and a matter-dominated Universe, in the regime in which the backreaction of the produced fermions on the axionic background can be neglected. 

The scalar and tensor fluctuations generated during inflation can be correlated, if arising from the same underlying mechanism. In this paper we investigate such correlation in the model of axion inflation, where the rolling inflaton produces quanta of a U(1) gauge field which, in turn, source scalar and tensor fluctuations. We compute the primordial correlator of the curvature perturbation, ζ, with the gravitational energy density, Ω_GW, at frequencies probed by gravitational wave detectors. This two-point function receives two contributions: one arising from the correlation of gravitational waves with the scalar perturbations generated by the standard mechanism of amplification of vacuum fluctuations, and the other coming from the correlation of gravitational waves with the scalar perturbations sourced by the gauge field. Our analysis shows that the former effect is generally dominant. For typical values of the parameters, the correlator, normalized by the amplitude of ζ and by the fractional energy in gravitational waves at interferometer frequencies, turns out to be of the order of 10^-4÷ 10^-2. 

We argue that the well-known beta functions of quadratic gravity do not correspond to the physical dependence of scattering amplitudes on external momenta, and derive the correct physical beta functions. Asymptotic freedom turns out to be compatible with the absence of tachyons. 

The scalar and tensor fluctuations produced during inflation can be correlated, if arising from the same underlying mechanism. In this paper we investigate such correlation in the model of axion inflation, where the rolling inflaton produces quanta of a U(1) gauge field which, in turn, source scalar and tensor fluctuations. We compute the primordial correlator of the curvature perturbation, ζ, with the amplitude of the gravitational waves squared, hijhij, at frequencies probed by gravitational wave detectors. This two-point function receives two contributions: one arising from the correlation of gravitational waves with the scalar perturbations generated by the standard mechanism of amplification of vacuum fluctuations, and the other coming from the correlation of gravitational waves with the scalar perturbations sourced by the gauge field. Our analysis shows that the latter effect is generally dominant. The correlator, normalized by the amplitude of ζ and of hijhij, turns out to be of the order of 10−2×(fequilNL)1/3, where fequilNL measures the scalar bispectrum sourced by the gauge modes. 

We explore the properties of a simple renormalizable shift-symmetric model with a higher-derivative kinetic energy and quartic-derivative coupling that can serve as a toy model for higher-derivative theories of gravity. The scattering amplitude behaves as in a normal effective field theory below the threshold for the production of ghosts, but has an unexpectedly soft behavior above the threshold. The physical running of the parameters is extracted from the two-point and four-point amplitudes. The results are compared to those obtained by other methods and are found to agree only in limiting cases. We draw several lessons that may also apply to gravity. 

Standard axion electrodynamics has two closely related features. First, the coupling of a massless axion field to photons is quantized, in units proportional to the electric gauge coupling squared. Second, the equations of motion tell us that a time-dependent axion field in a background magnetic field sources an effective electric current, but a time-dependent axion field in a background electric field has no effect. These properties, which manifestly violate electric-magnetic duality, play a crucial role in experimental searches for axions. Recently, electric-magnetic duality has been used to motivate the possible existence of non-standard axion couplings, which can both violate the usual quantization rule and exchange the roles of electric and magnetic fields in axion electrodynamics. We show that these non-standard couplings can be derived from SL(2,ℤ) duality, but that they come at a substantial cost: in non-standard axion electrodynamics, all electrically charged particles become dyons when the axion traverses its field range, in a dual form of the standard Witten effect monodromy. This implies that there are dyons near the weak scale, leads to a large axion mass induced by Standard Model fermion loops, and dramatically alters Higgs physics. We conclude that non-standard axion electrodynamics, although interesting to consider in abstract quantum field theory, is not phenomenologically viable. 

The Sharpened Distance Conjecture and Tower Scalar Weak Gravity Conjecture are closely related but distinct conjectures, neither one implying the other. Motivated by examples, I propose that both are consequences of two new conjectures: 1. The infinite distance geodesics passing through an arbitrary point ϕ in the moduli space populate a dense set of directions in the tangent space at ϕ. 2. Along any infinite distance geodesic, there exists a tower of particles whose scalar-charge-to-mass ratio (–∇log m) projection everywhere along the geodesic is greater than or equal to 1/√(d-2). I perform several nontrivial tests of these new conjectures in maximal and half-maximal supergravity examples. I also use the Tower Scalar Weak Gravity Conjecture to conjecture a sharp bound on exponentially heavy towers that accompany infinite distance limits.