Abstract
We determine the gluino condensate 〈Trλ2〉 in the pure N=1 super-Yang–Mills 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 instanton calculation.
Highlights
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), U Sp(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
In the first one [1], called the strong coupling instanton calculation, one evaluates the (r+1) point function Trλ2(x1) . . . Trλ2(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
A third elegant method [5] has been utilized in which one calculates the gaugino condensate directly in the semiclassical approximation, in the spacetime compactified on R3 × S1
Summary
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. 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.
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