Status report on the Instanton Counting
Abstract:
The non-perturbative behaviour of the N=2 supersymmetric Yang-Mills
theories is both highly non-trivial and tractible. 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, reprsenting
the effective action, to some finite dimensional conour 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 Ynag-Mills
theories. Almost all models with classical gauge groups, allowed by the
assymptotic 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.