M-theory five-brane wrapped on curves for exceptional groups

We study the M-theory five-brane wrapped around the Seiberg-Witten curves f or pure classical and exceptional groups given by an integrable system. Gen erically, the D3-branes arise as cuts that collapse to points after compact ifying the eleventh dimension and going to the semiclassical limit, produci ng brane configurations of NS5- and D4-branes with N = 2 gauge theories on the world volume of the four-branes. We study the symmetries of the differe nt curves to see how orientifold planes are related to the involutions need ed to obtain the distinguished Prym variety of the curve. This approach exp lains some subtleties encountered for the Sp(2n) and SO(2n + 1). Using this approach we investigate the curves for exceptional groups, especially G(2) and E-6, and show that unlike for classical groups taking the semiclassica l ten-dimensional limit does not reduce the cuts to D4-branes. For G(2) We find a genus-2 quotient curve that contains the Prym and has the right prop erties to describe the G(2) field theory, but the involutions are far more complicated than the ones for classical groups. To realize them in M-theory instead of an orientifold plane we would need another object, a kind of cu rved orientifold surface. (C) 1999 Elsevier Science B.V.