Universality of large N phase transitions in Wilson loop operators in two and three dimensions

Abstract

The eigenvalue distribution of a Wilson loop operator of fixed shape undergoes a transition under scaling at infinite N. We derive a large N scaling function in a double scaling limit of the average characteristic polynomial associated with the Wilson loop operator in two dimensional QCD. We hypothesize that the transition in three and four dimensional large N QCD are also in the same universality class and provide a numerical test for our hypothesis in three dimensions.

43 pages, 1 table, 18 figures, uses JHEP3.cls, one reference added, replaced Figure 3 and a small change to eqn (4.8)

References in corpus (2)

• Infinite N phase transitions in continuum Wilson loop operators
• Phases of three dimensional large N QCD on a continuum torus

Cited by in corpus (28)

• SU(N) gauge theories at large N
• Products of Rectangular Random Matrices: Singular Values and Progressive Scattering
• Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices
• Weak Commutation Relations and Eigenvalue Statistics for Products of Rectangular Random Matrices
• Introductory lectures to large-N QCD phenomenology and lattice results
• Large N_c confinement and turbulence
• Universal shocks in random matrix theory
• Burgers' equation in 2D SU(N) YM
• Gross-Witten-Wadia transition in a matrix model of deconfinement
• Wilson Loops and QCD/String Scattering Amplitudes
• Volume independence for Yang-Mills fields on the twisted torus
• Non-analyticity in scale in the planar limit of QCD
• Possible large-N transitions for complex Wilson loop matrices
• Complex Burgers' equation in 2D SU(N) YM
• Universal shocks in the Wishart random matrix ensemble - 1
• Numerical computation of the beta function of large N SU(N) gauge theory coupled to an adjoint Dirac fermion
• Eigenvalue density of Wilson loops in 2D SU(N) YM
• Burgers-like equation for spontaneous breakdown of the chiral symmetry in QCD
• Summing free unitary random matrices
• A large N phase transition in the continuum two dimensional SU(N) X SU(N) principal chiral model
• Two dimensional fermions in four dimensional YM
• The two-dimensional twisted reduced principal chiral model revisited
• Two dimensional fermions in three dimensional YM
• Topological order and the vacuum of Yang-Mills theories
• Confinement, Turbulence and Diffraction Catastrophes
• Narain transform for spectral deformations of random matrix models
• The equation of state of two dimensional Yang-Mills theory
• Scale invariant behavior in a large N matrix model