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arXiv · 2101.02226

Cosmological $\alpha'$-corrections from the functional renormalization group

Ivano Basile·Alessia Platania
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Abstract

We employ the techniques of the Functional Renormalization Group in string theory, in order to derive an effective mini-superspace action for cosmological backgrounds to all orders in the string scale $\alpha'$. To this end, T-duality plays a crucial role, classifying all perturbative curvature corrections in terms of a single function of the Hubble parameter. The resulting renormalization group equations admit an exact, albeit non-analytic, solution in any spacetime dimension $D$, which is however incompatible with Einstein gravity at low energies. Within an $\epsilon$-expansion about $D=2$, we also find an analytic solution which exhibits a non-Gaussian ultraviolet fixed point with positive Newton coupling, as well as an acceptable low-energy limit. Yet, within polynomial truncations of the full theory space, we find no evidence for an analog of this solution in $D=4$. Finally, we comment on potential cosmological implications of our findings.

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Ivano Basile, Alessia Platania. 2021-01-06. Cosmological $\alpha'$-corrections from the functional renormalization group. https://doi.org/10.1007/jhep06(2021)045

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