Spectral Curves for Super-Yang-Mills with Adjoint Hypermultiplet for General Lie Algebras

Abstract

The Seiberg-Witten curves and differentials for $\mathbb{N}=2$ supersymmetric Yang-Mills theories with one hypermultiplet of mass $m$ in the adjoint representation of the gauge algebra $\G$, are constructed for arbitrary classical or exceptional $\G$ (except $G_2$). The curves are obtained from the recently established Lax pairs with spectral parameter for the (twisted) elliptic Calogero-Moser integrable systems associated with the algebra $\G$. Curves and differentials are shown to have the proper group theoretic and complex analytic structure, and to behave as expected when $m$ tends either to 0 or to $\infty$. By way of example, the prepotential for $\G = D_n$, evaluated with these techniques, is shown to agree with standard perturbative results. A renormalization group type equation relating the prepotential to the Calogero-Moser Hamiltonian is obtained for arbitrary $\G$, generalizing a previous result for $\G = SU(N)$. Duality properties and decoupling to theories with other representations are briefly discussed.

27 pages, Plain TeX; minor typos corrected, 5 refs added

References in corpus (8)

• N=2 Supersymmetric Gauge Theories, Branes and Orientifolds
• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• Calogero-Moser Lax Pairs with Spectral Parameter for General Lie Algebras
• Multiscale N=2 SUSY field theories, integrable systems and their stringy/brane origin -- I
• Singular Monopoles and Supersymmetric Gauge Theories in Three Dimensions
• Calogero-Moser and Toda Systems for Twisted and Untwisted Affine Lie Algebras
• One Instanton Predictions of a Seiberg-Witten curve from M-theory: the Symmetric Representation of SU(N)
• Prepotentials and Riemann surfaces

Cited by in corpus (29)

• Baryons And Branes In Anti de Sitter Space
• Calogero-Moser Lax Pairs with Spectral Parameter for General Lie Algebras
• Calogero-Moser Models: A New Formulation
• Classification of 4d N=2 gauge theories
• Calogero-Moser Models II: Symmetries and Foldings
• Seiberg-Witten Geometries Revisited
• Calogero-Moser and Toda Systems for Twisted and Untwisted Affine Lie Algebras
• Instanton corrections in N=2 supersymmetric theories with classical gauge groups and fundamental matter hypermultiplets
• Seiberg--Witten Duality in Dijkgraaf--Vafa Theory
• Dirac pairings, one-form symmetries and Seiberg-Witten geometries
• Euler-Calogero-Moser system from SU(2) Yang-Mills theory
• Geometric construction of elliptic integrable systems and N=1^* superpotentials
• 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
• Lax Pairs and Spectral Curves for Calogero-Moser and Spin Calogero-Moser Systems
• Solutions to the reflection equation and integrable systems for N=2 SQCD with classical groups
• Seiberg-Witten Theory and Calogero-Moser Systems
• Duality in Topological Quantum Field Theories
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• On the Integrability of Four Dimensional N=2 Gauge Theories in the Omega Background
• Duality and Modularity in Elliptic Integrable Systems and Vacua of N=1* Gauge Theories
• The Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and their spectral curves
• 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
• Order Parameters, Free Fermions, and Conservation Laws for Calogero-Moser Systems
• Nonperturbative Recursion Relations in N=2 Supersymmetric Gauge Theories
• Global variants of $\mathcal{N}=1^{\ast }$ theories and Calogero-Moser systems