## LATEX

### N=2 supersymmetric gauge theory in D=4.....

-can we solve exactly quantum chromodynamics (QCD)..the gauge theory of the strong nuclear force...
-the answer is no...this is a highly non-perturbative theory..with highly non-trivial properties such confinement, the mass gap, chiral symmetry breaking and asymptotic freedom...
-But a trick was discovered to solve the theory..Namely, we add a lot of supersymmtery..more precisely, we add N=2 supersymmetry...
-The result is that the theory becomes soluble...this was shown in 1994 by Seiberg and Witten using holomorphy and supersymmetry..
-Nekarsov in 2002..rederived the Seiberg-Witten prepotential, which encodes the full low energy physics of the system, from microscopic considerations...
-he, Nekrasov, computed the path integral/partition integral of the system exactly and explicitly...
This is a spectacular result..
the prepotential was found to be equal to a perturbative part, computed from renormalization group consideration, and a non-perturbative part computed by summing up all instanton sectors...
Again, I say..this is a spectacular result...
It was the first time a sum over all instanton contributions of some gauge theory can be preformed so explicitly...
-Some of the technical machineries used by him to achieve this feat are:
1-supergravity, the so-called omega background, to regulate the infrared behaviour of the theory..
2-noncommutative geometry to smooth out the moduli space of instantons...