Breakdown of cluster decomposition in instanton calculations of the gluino condensate

Apr, 1999
29 pages
Published in:
  • Nucl.Phys.B 570 (2000) 241-266
e-Print:

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1999200520112017202302468
Abstract:
A longstanding puzzle concerns the calculation of the gluino condensate <{tr\lambda^2\over 16\pi^2}> = c\Lambda^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 <{tr\lambda^2\over 16\pi^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 <{tr\lambda^2\over 16\pi^2}> = 0) cannot straightforwardly resolve this mismatch.
  • gluino: condensation
  • gauge field theory: SU(N)
  • supersymmetry
  • instanton
  • strong coupling
  • weak coupling
  • n-point function
  • vacuum state
  • expansion 1/N