Inozemtsev System as Seiberg-Witten Integrable system

Abstract

In this work we establish that the Inozemtsev system is the Seiberg-Witten integrable system encoding the Coulomb branch physics of 4d $\mathcal{N}=2$ USp(2N) gauge theory with four fundamental and (for $N\ge 2$) one antisymmetric tensor hypermultiplets. We describe the transformation from the spectral curves and canonical one-form of the Inozemtsev system in the $N=1$ and $N=2$ cases to the Seiberg-Witten curves and differentials explicitly, along with the explicit matching of the modulus of the elliptic curve of spectral parameters to the gauge coupling of the field theory, and of the couplings of the Inozemtsev system to the field theory mass parameters. This result is a particular instance of a more general correspondence between crystallographic elliptic Calogero-Moser systems with Seiberg-Witten integrable systems, which will be explored in future work.

arXiv comment33 pages; comments are welcome

References in corpus (35)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• N=2 dualities
• Solutions Of Four-Dimensional Field Theories Via M Theory
• Supersymmetric Yang-Mills Systems And Integrable Systems
• F-theory and Orientifolds
• Integrability and Seiberg-Witten Exact Solution
• Integrable systems and supersymmetric gauge theory
• An N=2 Superconformal Fixed Point with E_6 Global Symmetry
• Webs of five-branes and N=2 superconformal field theories
• Superconformal Fixed Points with E_n Global Symmetry
• Probing F-theory With Branes
• Special Kahler Manifolds
• Holomorphic Bundles and Many-Body Systems
• A holographic computation of the central charges of d=4, N=2 SCFTs
• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• Integrable Structures in Supersymmetric Gauge and String Theory
• Calogero-Moser Lax Pairs with Spectral Parameter for General Lie Algebras
• N=2 Supersymmetric QCD and Integrable Spin Chains: Rational Case N_f < 2N_c
• Probing F-theory With Multiple Branes
• Exceptional Indices
• Multiscale N=2 SUSY field theories, integrable systems and their stringy/brane origin -- I
• Field Theory Questions for String Theory Answers
• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
• Painleve-Calogero Correspondence Revisited
• New N=2 superconformal field theories from M/F theory orbifolds
• Elliptic Linear Problem for Calogero-Inozemtsev Model and Painleve VI Equation
• N=2 SU Quiver with USP Ends or SU Ends with Antisymmetric Matter
• Reflection groups and 3d $\mathcal{N}\ge$ 6 SCFTs
• Quantum Lax pairs via Dunkl and Cherednik operators
• Elliptic Calogero-Moser Systems and Isomonodromic Deformations
• Calogero-Moser systems and Hitchin systems
• Noncommutative Painlevé equations and systems of Calogero type
• The M theory lift of two O6 planes and four D6 branes
• A Family of N=2 Gauge Theories with Exact S-Duality

Cited by in corpus (5)

• Gaudin Models and Multipoint Conformal Blocks: General Theory
• Gaudin Models and Multipoint Conformal Blocks II: Comb channel vertices in 3D and 4D
• Classical elliptic ${\mathrm{BC}}_1$ Ruijsenaars-van Diejen model: relation to Zhukovsky-Volterra gyrostat and 1-site classical XYZ model with boundaries
• R-matrix valued Lax pair for elliptic Calogero-Inozemtsev system and associative Yang-Baxter equations of ${\mathrm{BC}}_n$ type
• Complex crystallographic reflection groups and Seiberg-Witten integrable systems: rank 1 case