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No AbstractPublished by the Jagiellonian University2024authors 

A<sc>bstract</sc> We calculate the scattering amplitude in the two dimensionalCP(1) model in a regularization scheme independent way. When using cutoff regularization, a new Feynman rule from the path integral measure is required if one is to preserve the symmetry. The physical running of the coupling with renormalization scale arises from a UV finite Feynman integral in all schemes. We reproduce the usual result with asymptotic freedom, but the pathway to obtaining the beta function can be different in different schemes. The results can be extended to theO(N) model, for allN. We also comment on the way that this model evades the classic argument by Landau against asymptotic freedom in non-gauge theories. 

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.