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arXiv · hep-th/9904116

Breakdown of Cluster Decomposition in Instanton Calculations of the Gluino Condensate

T. J. Hollowood·V. V. Khoze·W. Lee·M. P. Mattis
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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.

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T. J. Hollowood, V. V. Khoze, W. Lee, M. P. Mattis. 1999-07-21. Breakdown of Cluster Decomposition in Instanton Calculations of the Gluino Condensate. https://doi.org/10.1016/s0550-3213(99)00503-9

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