paper

Breakdown of Cluster Decomposition in Instanton Calculations of the Gluino Condensate

arXiv:hep-th/9904116 · doi:10.1016/S0550-3213(99)00503-9

Abstract

A longstanding puzzle concerns the calculation of the gluino condensate <{trλ^2\over 16π^2}> = cΛ^3 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 <{trλ^2\over 16π^2}> 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 <{trλ^2\over 16π^2}> = 0) cannot straightforwardly resolve this mismatch.

31 pages, uses an avant-garde version of LaTeX; this version incorporates improved numerics as well as an enhanced discussion of the physics

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