Status Report on the Instanton Counting

Abstract

The non-perturbative behavior of the N=2 supersymmetric Yang-Mills theories is both highly non-trivial and tractable. In the last three years the valuable progress was achieved in the instanton counting, the direct evaluation of the low-energy effective Wilsonian action of the theory. The localization technique together with the Lorentz deformation of the action provides an elegant way to reduce functional integrals, representing the effective action, to some finite dimensional contour integrals. These integrals, in their turn, can be converted into some difference equations which define the Seiberg-Witten curves, the main ingredient of another approach to the non-perturbative computations in the N=2 super Yang-Mills theories. Almost all models with classical gauge groups, allowed by the asymptotic freedom condition can be treated in such a way. In my talk I explain the localization approach to the problem, its relation to the Seiberg-Witten approach and finally I give a review of some interesting results.

Talk given on the on the Sixth International Conference ``Symmetry in Nonlinear Mathematical Physics'' (June 20--26, 2005, Kyiv). Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (9)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Solutions Of Four-Dimensional Field Theories Via M Theory
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Geometric Engineering of Quantum Field Theories
• A note on instanton counting for N=2 gauge theories with classical gauge groups
• Saddle point equations in Seiberg-Witten theory
• On certain aspects of string theory/gauge theory correspondence
• The Coulomb Branch of N=2 Supersymmetric Product Group Theories from Branes
• M-Theory tested by N=2 Seiberg-Witten Theory

Cited by in corpus (7)

• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• Check of AGT Relation for Conformal Blocks on Sphere
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• From Brezin-Hikami to Harer-Zagier formulas for Gaussian correlators
• Challenges of beta-deformation
• Seiberg-Witten Geometry of Four-Dimensional $\mathcal{N}=2$ Quiver Gauge Theories