Breakdown of cluster decomposition in instanton calculations of the gluino condensate Original Research Article

A longstanding puzzle concerns the calculation of the gluino condensate trλ216π2=cΛ3 in N=1 supersymmetric SU(N) gauge theory: so-called weak-coupling instanton (WCI) calculations give c=1, whereas strong-coupling instanton (SCI) calculations give, instead, c=2(N−1)!(3N−1)−1/N. By examining correlators of this condensate in arbitrary multi-instanton sectors, we cast serious doubt on the SCI calculation of trλ216π2 by showing that an essential step—namely cluster decomposition—is invalid. We also show that the addition of a so-called Kovner-Shifman vacuum (in which trλ216π2=0) cannot straightforwardly resolve this mismatch.