Quantum Integrable Systems from Supergroup Gauge Theories

Abstract

In this note, we establish several interesting connections between the supergroup gauge theories and the super integrable systems, i.e. gauge theories with supergroups as their gauge groups and integrable systems defined on superalgebras. In particular, we construct the super-characteristic polynomials of super-Toda lattice and elliptic double Calogero-Moser system by considering certain orbifolded instanton partition functions of their corresponding supergroup gauge theories. We also derive an exotic generalization of sl(2) XXX spin chain arising from the instanton partition function of SQCD with supergauge group, and study its Bethe ansatz equation.

arXiv comment39 pages, 2 tables, fixed typo

References in corpus (31)

• The N=4 SYM Integrable Super Spin Chain
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Integrable systems and supersymmetric gauge theory
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Five Dimensional Gauge Theories and Relativistic Integrable Systems
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• Instanton counting with a surface operator and the chain-saw quiver
• Branes And Supergroups
• Negative Branes, Supergroups and the Signature of Spacetime
• Ghost D-branes
• Quiver W-algebras
• Spectral Duality in Integrable Systems from AGT Conjecture
• Spectral Duality Between Heisenberg Chain and Gaudin Model
• Quantization of Integrable Systems and a 2d/4d Duality
• A New 2d/4d Duality via Integrability
• Finite type modules and Bethe Ansatz for quantum toroidal gl(1)
• Magnificent Four with Colors
• Chern-Simons-Rozansky-Witten topological field theory
• Relating Gauge Theories via Gauge/Bethe Correspondence
• Superspace conformal field theory
• On Extensions of $\widehat{\mathfrak{gl}(m|n)}$ Kac-Moody algebras and Calabi-Yau Singularities
• Superspin chains and supersymmetric gauge theories
• Holomorphic field realization of SH${}^c$ and quantum geometry of quiver gauge theories
• Superanalogs of the Calogero operators and Jack polynomials
• Quantum Elliptic Calogero-Moser Systems from Gauge Origami
• Orthogonality of super-Jack polynomials and a Hilbert space interpretation of deformed Calogero-Moser-Sutherland operators
• Dynkin Diagrams and Integrable Models Based on Lie Superalgebras
• Topological Vertex/anti-Vertex and Supergroup Gauge Theory
• Matrix supergroup Chern-Simons models for vortex-antivortex systems

Cited by in corpus (9)

• Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations
• Higgsed network calculus
• Quantum Spin Systems and Supersymmetric Gauge Theories, I
• Intersecting Defects and Supergroup Gauge Theory
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• Defects and type D relativistic Toda lattice for some 5d gauge theories
• New dimer integrable systems and defects in five dimensional gauge theory
• Dimers for Type D Relativistic Toda Model