Remarks about the Yang-Mills Millennium problem

Yannick Meurice, PhD

In a recent Nature Reviews Physics on the Yang-Mills Millennium problem, Michael Douglas suggested that "Conceivably, the tensor RG [that we developed] will be adequate [to prove the conjecture], especially if it can accommodate duality arguments. We sketch three possible strategies to make progress along these lines: 1) design a model with a smaller gap and where the tensor RG can be applied easily, 2) reproduce the basic steps in numerical calculations of the gap, using dual variables with the tensor RG and try to find upper and lower bound on the gap, 3) reformulate the problem in terms of properties of the entanglement entropy which can estimated with the tensor RG. Note: the conjecture is the existence of a mass gap and is well supported by numerical approaches; RG means renormalization group, a coarse graining method.

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