7 papers
Anomalous symmetries in Kähler geometry
Dmitri Bykov, Andrew Kuzovchikov
We initiate a study of centrally extended () symmetries in Kähler geometry, focusing on the simplest, and most ubiquitous, Abelian case. In particular, we provi…
T-duality for toric manifolds in superspace
Dmitri Bykov, Savva Kutsubin, Andrew Kuzovchikov
We study the situation when the T-dual of a toric Kähler geometry is a generalized Kähler geometry involving semi-chiral fields. We explain that this situation is generic for pol…
Sigma models from Gaudin spin chains
Dmitri Bykov, Andrew Kuzovchikov
We solve the classical and quantum problems for the 1D sigma model with target space the flag manifold , equipped with the most general invarian…
Isotropic embeddings of coadjoint orbits and magnetic geodesic flows
Dmitri Bykov, Andrew Kuzovchikov
We consider isotropic and Lagrangian embeddings of coadjoint orbits of compact Lie groups into products of coadjoint orbits. After reviewing the known facts in the case of $\mathrm…
Mechanics on flag manifolds
Andrew Kuzovchikov
We study the connection between spin chains and one-dimensional sigma models on flag manifolds. Using this connection, we calculate the spectrum of the Laplace-Bel…
Oscillator Calculus on Coadjoint Orbits and Index Theorems
Dmitri Bykov, Viacheslav Krivorol, Andrew Kuzovchikov
We consider quantum mechanical systems of spin chain type, with finite-dimensional Hilbert spaces and or supersymmetry, described in …