Worldsheet functional RG and the α'-tower
Abstract
We apply the functional renormalization group to the worldsheet theory of the bosonic string. Imposing the Weyl anomaly cancellation as a condition on the local renormalization group flow, we derive flow equations for the background couplings and the corresponding effective spacetime equations of motion, first in a two-derivative truncation, on a general curved background. We then consider a truncation to all orders in α', which captures only a subset of the possible tensor structures but is analytically tractable, in analogy with f(R)-like approximations. Within this truncation, we obtain Tseytlin's spacetime effective action, and we use it to study solutions to all orders in α', including black holes. Our results show that the functional renormalization group can be implemented on the string worldsheet and provide a framework to access the strong-curvature regime. As a longer-term goal, this may allow one to test the scenario of effective asymptotic safety in string theory, in which an approximately scale-invariant regime lies between the low-energy effective field theory and a stringy completion.
Related
BibTeX
@misc{basile2026worldsheet,
title = {{Worldsheet functional RG and the $α'$-tower}},
author = {Ivano Basile and Francesco Ferrarin and Alessia Platania and Matteo Zatti},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03781},
eprint = {2611.03781},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03781},
}
RIS
TY - UNPB
TI - Worldsheet functional RG and the α'-tower
AU - Ivano Basile
AU - Francesco Ferrarin
AU - Alessia Platania
AU - Matteo Zatti
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03781
UR - https://arxiv.org/abs/2611.03781
AB - We apply the functional renormalization group to the worldsheet theory of the bosonic string. Imposing the Weyl anomaly cancellation as a condition on the local renormalization group flow, we derive flow equations for the background couplings and the corresponding effective spacetime equations of motion, first in a two-derivative truncation, on a general curved background. We then consider a truncation to all orders in α', which captures only a subset of the possible tensor structures but is analytically tractable, in analogy with f(R)-like approximations. Within this truncation, we obtain Tseytlin's spacetime effective action, and we use it to study solutions to all orders in α', including black holes. Our results show that the functional renormalization group can be implemented on the string worldsheet and provide a framework to access the strong-curvature regime. As a longer-term goal, this may allow one to test the scenario of effective asymptotic safety in string theory, in which an approximately scale-invariant regime lies between the low-energy effective field theory and a stringy completion.
ER -