Infinite N phase transitions in continuum Wilson loop operators

Abstract

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 Lambda-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.

31 pages, 9 figures, typos and references corrected, minor clarifications added

References in corpus (2)

• Universal Subleading Spectrum of Effective String Theory
• Phase transitions and non-analyticities in large N gauge theories

Cited by in corpus (7)

• Burgers' equation in 2D SU(N) YM
• Complex Burgers' equation in 2D SU(N) YM
• A large N phase transition in the continuum two dimensional SU(N) X SU(N) principal chiral model
• A Linear Equation for Wilson Loops
• Tunneling in two dimensional QCD
• Large N lattice gauge theory
• Matching of Wilson loop eigenvalue densities in 1+1, 2+1 and 3+1 dimensions