By F. Wilczek

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Indeed, we can think of it as multiplying different triality sectors containing N quarks, (modulo N for SU(N)) by different phases. ‘Virtual’ quark worldlines winding around the imaginary time circle are not left invariant. Indeed, with the implementation above, terms in the action that hop quarks from τ = 0 to τ = a are not invariant. By redefining ψ(τ = a) by a phase you can move the changes in the action to the next time slice, ... , but after winding around the circle you will just arrive back where you started.

The quality of the present √ NA49 data, and the confidence with which we can use it to learn that collisions at s = 17 GeV 17 GeV do not freeze out near the critical point make it plausible that critical behavior, if present, could be discerned experimentally. If and when the critical point P is discovered, it will appear prominently on the map of the phase diagram featured in any future textbook of QCD. 3. Wanted: Numerical Data The web of general arguments I have outlined above seems to me to make it quite plausible that there is a true critical point in QCD.

54 M is actually subject to catastrophic fluctuations, that change the structure of the problem qualitatively. Thus the renormalization group fails to identify a consistent model for a second order transition, and indicates instead that the transition must be a first order transition. In important work Gausterer and Sanielevici have simulated the f = 3 matrix models directly, both with and without the determinantal interaction, to search for second-order transitions. None was found; the transition is always first order.