https://neckpinch.com/authors/dmitri-bykov/New arXiv papers by Dmitri Bykov, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2106.15598/arxiv:2106.15598Tue, 29 Jun 2021 00:00:00 GMTDmitri Bykov — We review the correspondence between integrable sigma models with complex homogeneous target spaces and chiral bosonic (and possibly mixed bosonic/fermionic) Gross-Neveu models. Mathematically, the latter are models with quiver variety phase spaces, which reduce to the more conventional sigma models in special cases. We discuss the geometry of the models, as well as their trigonometric and elliptic deformations, Ricci flow and the inclusion of fermions.Ricci flowHomogeneous spacesPhysics https://neckpinch.com/papers/2101.11638/arxiv:2101.11638Wed, 27 Jan 2021 00:00:00 GMTIan Affleck, Dmitri Bykov, Kyle Wamer — This review is dedicated to two-dimensional sigma models with flag manifold target spaces, which are generalizations of the familiar CPⁿ⁻¹ and Grassmannian models. They naturally arise in the description of continuum limits of spin chains, and their phase structure is sensitive to the values of the topological angles, which are determined by the representations of spins in the chain. Gapless phases can in certain cases be explained by the presence of discrete 't Hooft anomalies in the continuum theory. We also discuss integrable flag manifold sigma models, which provide a generalization of the theory of integrable models with symmetric target spaces. These models, as well as their deformations, have an alternative equivalent formulation as bosonic Gross-Neveu models, which proves useful for demonstrating that the deformed geometries are solutions of the renormalization group (Ricci flow) equations, as well as for the analysis of anomalies and for describing potential couplings to fermions.Ricci flowSurfacesPhysics https://neckpinch.com/papers/2006.14124/arxiv:2006.14124Thu, 25 Jun 2020 00:00:00 GMTDmitri Bykov — We show that flag manifold σ-models (including ℂP}ⁿ⁻¹, Grassmannian models as special cases) and their deformed versions may be cast in the form of gauged bosonic Thirring/Gross-Neveu-type systems. Quantum mechanically the gauging is violated by chiral anomalies, which may be cancelled by adding fermions. We conjecture that such models are integrable and check on some examples that the trigonometrically deformed geometries satisfy the generalized Ricci flow equations.Ricci flowGeneralized & G₂ flows https://neckpinch.com/papers/2005.01812/arxiv:2005.01812Mon, 04 May 2020 00:00:00 GMTDmitri Bykov, Dieter Lust — It is shown that the Pohlmeyer map of a σ-model with a toric two-dimensional target space naturally leads to the `sausage' metric. We then elaborate the trigonometric deformation of the CPⁿ⁻¹-model, proving that its T-dual metric is Kähler and solves the Ricci flow equation. Finally, we discuss a relation between flag manifold σ-models and Toda field theories.Ricci flowSurfacesKähler geometry