LEEA in 4d, N = 2 Gauge Field Theories

Abstract

Non-perturbative solutions to the Low-Energy Effective Action (LEEA) in four-dimensional (4d), N = 2 supersymmetric gauge field theories can be obtained either by QFT methods (e.g., using a strong-weak coupling duality), or by the Type-IIA superstring/M-theory methods of brane technology (Sect. 8.4). In this chapter we review the field-theoretical results about the N = 2 gauge (Seiberg-Witten) LEEA (Sect. 8.2) and the hypermultiplet LEEA (Sect. 8.3). We also introduce the alternative methods of brane technology (Sect. 8.4). The latter are based on the exact solutions to the 11d and 10d type-IIA supergravities, which describe classical configurations of intersecting BPS branes with eight conserved supercharges (the same number as in 4d, N = 2 supersymmetry). The crucial role of M-theory in providing the classical resolution of singularities in the 10-dimensional (Type-IIA superstring) brane picture is made manifest. The existing methods of derivation of the exact LEEA in 4d, N = 2 gauge field theories are shown to be complementary to each other.