The sausage sigma model revisited

Abstract

Fateev's sausage sigma models in two and three dimensions are known to be integrable. We study their stability under RG flow in the target space by using results from the mathematics of Ricci flow. We show that the three dimensional sausage is unstable, whereas the two dimensional sausage appears to be stable at least at leading order as it approaches the sphere. We speculate that the stability results obtained are linked to the classification of ancient solutions to Ricci flow (i.e., sigma models which are nonperturbative in the IR) in two and three dimensions. We also describe a class of perturbations of the three dimensional sausage (with the same continuous symmetries) which remarkably decouple. This indicates that there could be a new solution to RG flow which is described at least perturbatively as a deformation of the sausage.

arXiv comment23 pages, 1 figure, journal version

References in corpus (11)

• On integrability of the Yang-Baxter $\si$-model
• Stability of Higher-Dimensional Schwarzschild Black Holes
• On deformations of AdS_n x S^n supercosets
• Integrability of the bi-Yang-Baxter sigma-model
• Ricci flow and black holes
• Closed String Tachyon Condensation: An Overview
• The integrable harmonic map problem versus Ricci flow
• ODE/IM correspondence for the Fateev model
• Stability analysis of the Witten black hole (cigar soliton) under world-sheet RG flow
• Winding vacuum energies in a deformed O(4) sigma model
• Investigating stability of a class of black hole spacetimes under Ricci flow

Cited by in corpus (2)

• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Poisson-Lie T-duals of the bi-Yang-Baxter models