Calogero-Moser Systems in SU(N) Seiberg-Witten Theory

Abstract

The Seiberg-Witten curve and differential for $\mathcal{N}=2$ supersymmetric SU(N) gauge theory, with a massive hypermultiplet in the adjoint representation of the gauge group, are analyzed in terms of the elliptic Calogero-Moser integrable system. A new parametrization for the Calogero-Moser spectral curves is found, which exhibits the classical vacuum expectation values of the scalar field of the gauge multiplet. The one-loop perturbative correction to the effective prepotential is evaluated explicitly, and found to agree with quantum field theory predictions. A renormalization group equation for the variation with respect to the coupling is derived for the effective prepotential, and may be evaluated in a weak coupling series using residue methods only. This gives a simple and efficient algorithm for the instanton corrections to the effective prepotential to any order. The 1- and 2- instanton corrections are derived explicitly. Finally, it is shown that certain decoupling limits yield $\mathcal{N}=2$ supersymmetric theories for simple gauge groups $SU(N_1)$ with hypermultiplets in the fundamental representation, while others yield theories for product gauge groups $SU(N_1)\times ...\times SU(N_p)$, with hypermultiplets in fundamental and bi-fundamental representations. The spectral curves obtained this way for these models agree with the ones proposed by Witten using D-branes and M-theory.

45 pages, Tex, no figures

Cited by in corpus (77)

• Matrix Models, Geometric Engineering and Elliptic Genera
• Calogero-Moser Lax Pairs with Spectral Parameter for General Lie Algebras
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Non-Abelian Vortices in N=1* Gauge Theory
• Unoriented Strings, Loop Equations, and N=1 Superpotentials from Matrix Models
• Saddle point equations in Seiberg-Witten theory
• The Ruijsenaars-Schneider Model in the Context of Seiberg-Witten Theory
• Instanton Expansions for Mass Deformed N=4 Super Yang-Mills Theories
• Spectral Curves for Super-Yang-Mills with Adjoint Hypermultiplet for General Lie Algebras
• Calogero-Moser and Toda Systems for Twisted and Untwisted Affine Lie Algebras
• The toroidal block and the genus expansion
• A_N-type Dunkl operators and new spin Calogero-Sutherland models
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• N=1 Superpotentials from Multi-Instanton Calculus
• New spin Calogero-Sutherland models related to B_N-type Dunkl operators
• Instanton corrections in N=2 supersymmetric theories with classical gauge groups and fundamental matter hypermultiplets
• The Curve of Compactified 6D Gauge Theories and Integrable Systems
• On the equivalence of the rational Calogero-Moser system to free particles
• Exact solutions of an elliptic Calogero--Sutherland model
• Seiberg--Witten Duality in Dijkgraaf--Vafa Theory
• Quantum Spin Systems and Supersymmetric Gauge Theories, I
• Testing Seiberg-Witten Theory to All Orders in the Instanton Expansion
• Dirac pairings, one-form symmetries and Seiberg-Witten geometries
• Quantum Elliptic Calogero-Moser Systems from Gauge Origami
• $\mathcal{N}=2^{\ast }$ gauge theory, free fermions on the torus and Painlevé VI
• One-instanton predictions for non-hyperelliptic curves derived from M-theory
• Free harmonic oscillators, Jack polynomials and Calogero-Sutherland systems
• Calogero model, deformed oscillators and the collapse
• On the Sutherland Spin Model of B_N Type and its Associated Spin Chain
• Elliptic models and M-theory
• Euler-Calogero-Moser system from SU(2) Yang-Mills theory
• Modular and duality properties of surface operators in N=2* gauge theories
• Integrable Hierarchies and Contact Terms in u-plane Integrals of Topologically Twisted Supersymmetric Gauge Theories
• On the Quantization of Seiberg-Witten Geometry
• Lax Pairs and Spectral Curves for Calogero-Moser and Spin Calogero-Moser Systems
• Seiberg-Witten Theory and Integrable Systems
• Effective gravitational couplings of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories
• The N=1* Theories on R^{1+2} X S^1 with Twisted Boundary Conditions
• Singular Phases of Seiberg-Witten Integrable Systems: Weak and Strong Coupling
• Seiberg-Witten Theory and Calogero-Moser Systems
• Solvable scalar and spin models with near-neighbors interactions
• Quantum Integrable Systems from Supergroup Gauge Theories
• A Unified Algebraic Approach to Few and Many-Body Correlated Systems
• The Coulomb branch of the Leigh-Strassler deformation and matrix models
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Duality in Integrable Systems and Generating Functions for New Hamiltonians
• Duality in Topological Quantum Field Theories
• Two antisymmetric hypermultiplets in N=2 SU(N) gauge theory: Seiberg-Witten curve and M-theory interpretation
• On the WDVV Equation and M-Theory
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• Gauge origami and quiver W-algebras
• One-instanton predictions of Seiberg-Witten curves for product groups
• Exchange operator formalism for N-body spin models with near-neighbors interactions
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Towards Lefschetz thimbles in Sigma models, I
• Inozemtsev System as Seiberg-Witten Integrable system
• Modular properties of 6d (DELL) systems
• New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
• Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories
• Holographic RG Flows and Universal Structures on the Coulomb Branch of N=2 Supersymmetric Large n Gauge Theory
• WDVV equation and Triple-product Relation
• On the Geometry of Matrix Models for N=1*
• Effective Gravitational Couplings of Higher-Rank Supersymmetric Gauge Theories
• Exact quantization conditions for the elliptic Ruijsenaars-Schneider model
• Topological correlators of $SU(2)$, $\mathcal{N}=2^{\ast }$ SYM on four-manifolds
• Matone's relation of N=2 super Yang-Mills and spectrum of Toda chain
• Instanton Correction of Prepotential in Ruijsenaars Model Associated with N=2 SU(2) Seiberg-Witten Theory
• Prepotential Recursion Relations in N=2 Super-Yang Mills with Adjoint Matter
• The Prepotential of N=2 SU(2) x SU(2) Supersymmetric Yang-Mills Theory with Bifundamental Matter
• M-Theory Five-brane Wrapped on Curves for Exceptional Groups
• Generalized Calogero-Moser system and supergroup gauge origami
• The Dynamical Yang-Baxter Relation and the Minimal Representation of the Elliptic Quantum Group
• Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials
• Novikov-Veselov Symmetries of the Two-Dimensional $O(N)$ Sigma Model
• 3-Algebraic structures of the quantum Calogero-Moser model
• Periodic and almost periodic potentials in the inverse problems
• Novel wall-crossing behaviour in rank one $\mathcal{N}=2^{\ast }$ gauge theory