Calculating Gluino Condensates in N = 1 SYM from Seiberg-Witten Curves

We determine the gluino condensate 〈 Trλ2 〉 in the pure N = 1 super YangMills theory (SYM) for the classical gauge groups SU(r+1), SO(2r+1), USp(2r) and SO(2r), by deforming the pure N = 2 SYM theory with the adjoint scalar multiplet mass, following the work by Finnell and Pouliot, and Ritz and Vainshtein. The value of the gluino condensate agrees in all cases with what was found in the weak coupling istanton calculation. The value of the gluino condensate in the pure N = 1 super Yang-Mills theory with gauge group SU(r + 1) has been calculated in the eighties by using two different methods. In the first one [1], called the strong coupling instanton calculation, one evaluates the (r+1) point function 〈 Trλ(x1) . . .Trλ (xr+1) 〉 which is saturated by one instanton zero modes at short distances, and being constant due to supersymmetric Ward-Takahashi identities, it is set equal to the product of 〈 Trλ2 〉 by clustering. The second method [2], the so-called weak coupling istanton calculation, makes use of a deformation of the original theory by addition of some matter fields. Classically, the [email protected] [email protected]