Peter Koroteev

Quantum Deformations of the One-Dimensional Hubbard Model

The centrally extended superalgebra psu(2|2) �R 3 was shown to play an important role for the integrable structures of the one-dimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation Uq(psu(2|2) �R 3 ) and derive the fundamentalR-matrix. From the latter we deduce an integrable spin-chain Hamiltonian with three independent parameters and the corresponding Bethe equations to describe the spectrum on periodic chains. We relate our Hamiltonian to a two-parametric Hamiltonian proposed by Alcaraz and Bariev which can be considered a quantum deformation of the one-dimensional Hubbard model.

On three dimensional quiver gauge theories and integrability

A bstractIn this work we compare different descriptions of the space of vacua of certain three dimensional

Defects and Quantum Seiberg-Witten Geometry

\mathcal{N}=4

BPS states in omega background and integrability

superconformal field theories, compactified on a circle and mass-deformed to

Spectra of field fluctuations in braneworld models with broken Lorentz invariance

\mathcal{N}=2

Mirror symmetry in three dimensions via gauged linear quivers

in a canonical way. The original

Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories

\mathcal{N}=4

On elliptic algebras and large-n supersymmetric gauge theories

theories are known to admit two distinct mirror descriptions as linear quiver gauge theories, and many more descriptions which involve the compactification on a segment of four-dimensional

On the integrability of four dimensional \mathcal{N}=2 gauge theories in the omega background

\mathcal{N}=4

Statistical mechanics of Coulomb gases as quantum theory on Riemann surfaces

super Yang-Mills theory. Each description gives a distinct presentation of the moduli space of vacua. Our main result is to establish the precise dictionary between these presentations. We also study the relationship between this gauge theory problem and integrable systems. The space of vacua in the linear quiver gauge theory description is related by Nekrasov-Shatashvili duality to the eigenvalues of quantum integrable spin chain Hamiltonians. The space of vacua in the four-dimensional gauge theory description is related to the solution of certain integrable classical many-body problems. Thus we obtain numerous dualities between these integrable models.