Ricci flows and expansion in axion-dilaton cosmology

Abstract

We study renormalization-group flows by deforming a class of conformal sigma-models. We consider overall scale factor perturbation of Einstein spaces as well as more general anisotropic deformations of three-spheres. At leading order in alpha, renormalization-group equations turn out to be Ricci flows. In the three-sphere background, the latter is the Halphen system, which is exactly solvable in terms of modular forms. We also analyze time-dependent deformations of these systems supplemented with an extra time coordinate and time-dependent dilaton. In some regimes time evolution is identified with renormalization-group flow and time coordinate can appear as Liouville field. The resulting space-time interpretation is that of a homogeneous isotropic Friedmann-Robertson-Walker universe in axion-dilaton cosmology. We find as general behaviour the superposition of a big-bang (polynomial) expansion with a finite number of oscillations at early times. Any initial anisotropy disappears during the evolution.

22 pages

References in corpus (2)

• Ricci flow and black holes
• Closed String Tachyon Condensation in Supercritical Strings and RG Flows

Cited by in corpus (5)

• Yangian symmetry in deformed WZNW models on squashed spheres
• Geometric flows in Horava-Lifshitz gravity
• Gravitational instantons, self-duality and geometric flows
• Axion-dilaton cosmology, Ricci flows and integrable structures
• Integrability and renormalizability for the fully anisotropic $\mathrm{SU}(2)$ principal chiral field and its deformations