  Exact solutions to the low-energy effective action (LEEA) of the
four-dimensional N=2 supersymmetric gauge field theories are known to be
obtained either by quantum field theory methods from S-duality in the
Seiberg-Witten approach, or by the Type-IIA superstring/M-Theory methods of
brane technology. After a brief review of the standard field-theoretical
results for the N=2 gauge (Seiberg-Witten) LEEA, we consider a
field-theoretical derivation of the exact hypermultiplet LEEA by using the N=2
harmonic superspace methods. We illustrate our techniques on a number of
explicit examples. Our main purpose, however, is to discuss the existing
analytical (calculational) support for the alternative methods of brane
technology. We summarize known exact solutions to the eleven-dimensional and
ten-dimensional type-IIA supergravities, which describe classical
configurations of intersecting BPS branes with eight supercharges relevant to
the non-perturbative N=2 gauge field theory with fundamental hypermultiplet
matter. The crucial role of M-Theory in providing a classical resolution of
singularities in the ten-dimensional (Type-IIA superstring) brane picture, as
well as the N=2 extended supersymmetry in four dimensions, are made manifest.
The two approaches to a derivation of the exact N=2 gauge theory LEEA are thus
seen to be complementary to each other and mutually dependent.

High Energy Physics - Theory