Spontaneous Parity Violation
  We disprove the Vafa-Witten theorem on the impossibility of spontaneously breaking parity in vector-like gauge field theories, identifying a mechanism driven by quantum fluctuations. With the introduction of a meromorphic Lattice formulation, defined over 5 dimensions, we demonstrate that the minima of the free energy can be distinct from the maxima of the partition function : identifying and evaluating a suitable contour for the partition function defined such that asymptotic behaviour of the complex action is non-oscillatory. 
P.R. Crompton