https://neckpinch.com/authors/nat-levine/New arXiv papers by Nat Levine, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2112.03928/arxiv:2112.03928Tue, 07 Dec 2021 00:00:00 GMTNat Levine — Motivated by the search for solvable string theories, we consider the problem of classifying the integrable bosonic 2d σ-models. We include non-conformal σ-models, which have historically been a good arena for discovering integrable models that were later generalized to Weyl-invariant ones. General σ-models feature a quantum RG flow, given by a 'generalized Ricci flow' of the target-space geometry. This thesis is based on the conjecture that integrable σ-models are renormalizable, or stable under the RG flow. It is widely understood that classically integrable theories are stable at the leading 1-loop order with only a few parameters running. Here we address what happens at higher-loop orders. We find that integrable σ-models generally remain RG-stable at higher-loops provided they receive a particular choice of finite counterterms, or quantum (α') corrections to the target-space geometry. We explicitly construct these quantum corrections for examples of integrable η- and λ-deformed σ-models. We then reformulate the λ-models as σ-models on a "tripled" G × G × G configuration space, where they become automatically renormalizable due to manifest symmetries and a decoupling of some fields. We also consider the integrable G × G and G × G/H models and construct a new class of integrable G × G/H models with abelian H. We then present a new and different link between integrability and the RG flow in the context of σ-models with 'local couplings' depending explicitly on 2d time. Such models are naturally obtained in the light-cone gauge in string theory, pointing to the possibility of a large, new class of solvable string models.Ricci flowGeneralized & G₂ flowsHomogeneous spacesPhysics