Isomonodromic Properties of the Seiberg-Witten Solution

Abstract

The Seiberg-Witten solution of N=2 supersymmetric SU(2) gauge theories with matter is analysed as an isomonodromy problem. We show that the holomorphic section describing the effective action can be deformed by moving its singularities on the moduli space while keeping their monodromies invariant. Well-known examples of isomonodromic sections are given by the correlators of two-dimensional rational conformal field theories -- the conformal blocks. The Seiberg-Witten section similarly admits the operations of braiding and fusing of its singularities, which obey the Yang-Baxter and Pentagonal identities, respectively. Using them, we easily find the complete expressions of the monodromies with affine term, and the full quantum numbers of the BPS spectrum. While the braiding describes the quark-monopole transmutation, the fusing implies the superconformal points in the moduli space. In the simplest case of three singularities, the supersymmetric sections are directly related to the conformal blocks of the logarithmic minimal models.

Latex, 40 pages, 9 eps figures. Correction of misprints only

References in corpus (3)

• Duality in Supersymmetric Yang-Mills Theory
• The dyon spectra of finite gauge theories
• Flat Coordinates, Topological Landau-Ginzburg Models and the Seiberg-Witten Period Integrals

Cited by in corpus (18)

• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• Bits and Pieces in Logarithmic Conformal Field Theory
• The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
• Seiberg-Witten theory for a non-trivial compactification from five to four dimensions
• Logarithmic Conformal Field Theory and Seiberg-Witten Models
• SU(2)_0 and OSp(2|2)_{-2} WZNW models : Two current algebras, one Logarithmic CFT
• Legendre's Relation and the Quantum Equivalence osp(4|4)_(1) = osp(2|2)_(-2) + su(2)_(0)
• Non Abelian Magnetic Monopoles and Dynamics of Confinement
• The Holomorphic Tension of Vortices
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Dynamical Abelianization and anomalies in chiral gauge theories
• Nonabelian Confinement near Nontrivial Conformal Vacua
• Extended chiral algebras in the SU(2)_0 WZNW model
• Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas
• Almost Conformal Vacua and Confinement
• Extended multiplet structure in Logarithmic Conformal Field Theories
• Stress Energy tensor in LCFT and the Logarithmic Sugawara construction
• Pure Gauge SU(2) Seiberg-Witten Theory and Modular Forms