Infinite N phase transitions in continuum Wilson loop operators

By R. Narayanan, H. Neuberger. 2006

323 citations recorded by the source corpus.

We define smoothed Wilson loop operators on a four dimensional lattice and check numerically that they have a finite and nontrivial continuum limit. The continuum operators maintain their character as unitary matrices and undergo a phase transition at infinite N reflected by the eigenvalue distribution closing a gap in its spectrum when the defining smooth loop is dilated from a small size to a large one. If this large N phase transition belongs to a solvable universality class one might be able to calculate analytically the string tension in terms of the perturbative Λ-parameter. This would be achieved by matching instanton results for small loops to the relevant large-N-universal function which, in turn, would be matched for large loops to an effective string theory. Similarities between our findings and known analytical results in two dimensional space-time indicate that the phase transitions we found only affect the eigenvalue distribution, but the traces of finite powers of the Wilson loop operators stay smooth under scaling.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/af6f56d7b17c07f02c04904139d536d3d49c3183

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Citations in the corpus

Simulation of QCD with Nf = 2 + 1 flavors of non-perturbatively improved Wilson fermions (2014, methodology): “The Wilson flow can be a very useful tool in lattice QCD from which quantities with a finite continuum limit can be constructed [6, 56, 57].”
FLAG Review 2019 (2019, background): “The gradient flow is introduced as follows [271, 715].”
High-precision scale setting in lattice QCD (2012, methodology): “It was studied earlier by Narayanan and Neuberger [11] in a different context, too.”