Complex Burgers' equation in 2D SU(N) YM
arXiv:0809.1238 · doi:10.1016/j.physletb.2008.11.009
Abstract
An integro-differential equation satisfied by an eigenvalue density defined as the logarithmic derivative of the average inverse characteristic polynomial of a Wilson loop in two dimensional pure Yang Mills theory with gauge group SU(N) is derived from two associated complex Burgers' equations, with viscosity given by 1/(2N). The Wilson loop does not intersect itself and Euclidean space-time is assumed flat and infinite. This result provides an extension of the infinite N solution of Durhuus and Olesen to finite N, but this extension is not unique.
10 pages; fixed typo in eq. 37, updated 1 reference and added 2 minor clarifying comments
References in corpus (5)
- Infinite N phase transitions in continuum Wilson loop operators
- Large N_c confinement and turbulence
- Universality of large N phase transitions in Wilson loop operators in two and three dimensions
- 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
Cited by in corpus (13)
- SU(N) gauge theories at large N
- Dysonian dynamics of the Ginibre ensemble
- Introductory lectures to large-N QCD phenomenology and lattice results
- Unveiling the significance of eigenvectors in diffusing non-hermitian matrices by identifying the underlying Burgers dynamics
- Universal shocks in random matrix theory
- Universal shocks in the Wishart random matrix ensemble - 1
- Eigenvalue density of Wilson loops in 2D SU(N) YM
- Handbook Article on Applications of Random Matrix Theory to QCD
- Integrable models from PT-symmetric deformations
- Diffusion method in Random Matrix Theory
- Current fluctuations in the Dyson Gas
- Functional Equations Solving Initial-Value Problems of Complex Burgers-Type Equations for One-Dimensional Log-Gases
- Eigenvalue density of Wilson loops in 2D SU(N) YM at large N