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SIGMA 2 (2006), 008, 11 pages hep-th/0601167
https://doi.org/10.3842/SIGMA.2006.008
Status Report on the Instanton Counting
Sergey Shadchin
INFN, Sezione di Padova & Dipartimento di Fisica
“G. Galilei”, Università degli Studi di Padova, via F. Marzolo 8, Padova, 35131, Italy
Received December 07, 2005, in final form January 18, 2006; Published online January 22, 2006
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.
Key words:
instanton counting; Seiberg-Witten theory.
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