Cosmological α′-corrections from the functional renormalization group

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 E-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.

Automated summary

In this study, the Functional Renormalization Group techniques were applied in string theory to derive an effective mini-superspace action for cosmological backgrounds in terms of the string scale alpha '. T-duality played a crucial role in classifying perturbative curvature corrections, leading to renormalization group equations with exact solutions in any spacetime dimension D. While an analytic solution with a non-Gaussian ultraviolet fixed point was found around D = 2, no analogous solution was found in D = 4 using polynomial truncations. The study also discussed potential cosmological implications of the findings.