2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/180623In this work we study renormalization-group flows by deforming a class of conformal sigma-models. At leading order in $α'$, renormalization-group equations represent a Ricci flow. In the three-sphere background, the latter is described by the Halphen system, which is exactly solvable in terms of modular forms. The round sphere is found to be the unique perturbative infra-red fixed point at one loop order.2 pages, based on a talk given at the Cargese Summer School, May 22 to June 3, 2006High Energy Physics - Theorytext