  The conventional double-scaling limit of an O(N)-symmetric quartic quantum
field theory is inconsistent because the critical coupling constant is
negative. Thus, at the critical coupling the Lagrangian defines a quantum
theory with an upside-down potential whose energy appears to be unbounded
below. Worse yet, the integral representation of the partition function of the
theory does not exist. It is shown that one can avoid these difficulties if one
replaces the original theory by its PT-symmetric analog. For a zero-dimensional
O(N)-symmetric quartic vector model the partition function of the PT-symmetric
analog is calculated explicitly in the double-scaling limit.
