Breakdown of cluster decomposition in instanton calculations of the gluinocondensate

A longstanding puzzle concerns the calculation of the gluino condensate [tr lambda(2)/16 pi(2)] = c Lambda(3) in N = 1 supersymmetric SU(N) gauge theo ry: so-called weak-coupling instanton (WCI) calculations give c = 1, wherea s strong-coupling instanton (SCI) calculations give, instead, c = By examin ing correlators of this condensate in arbitrary multi-instanton sectors, we cast serious doubt on the SCI calculation of [tr lambda(2)/16 pi(2)] by sh owing that an essential step-namely cluster decomposition-is invalid. We al so show that the addition of a so-called Kovner-Shifman vacuum (in which [t r lambda(2)/16 pi(2)] = 0) cannot straightforwardly resolve this mismatch. (C) 2000 Elsevier Science B.V. All rights reserved.