A loop of SU(2) gauge fields stable under the Yang-Mills flow
Abstract
The gradient flow of the Yang-Mills action acts pointwise on closed loops of gauge fields. We construct a topologically nontrivial loop of SU(2) gauge fields on S4 that is locally stable under the flow. The stable loop is written explicitly as a path between two gauge fields equivalent under a topologically nontrivial SU(2) gauge transformation. Local stability is demonstrated by calculating the flow equations to leading order in perturbations of the loop. The stable loop might play a role in physics as a classical winding mode of the lambda model, a 2-d quantum field theory that was proposed as a mechanism for generating spacetime quantum field theory. We also present evidence for 2-manifolds of SU(2) and SU(3) gauge fields that are stable under the Yang-Mills flow. These might provide 2-d instanton corrections in the lambda model. For Isidore M. Singer in celebration of his eighty-fifth birthday.
Keywords
Cite
@article{arxiv.1008.1189,
title = {A loop of SU(2) gauge fields stable under the Yang-Mills flow},
author = {Daniel Friedan},
journal= {arXiv preprint arXiv:1008.1189},
year = {2010}
}
Comments
55 pages, 7 figures. Version 2. Added sections 12.2.9-10 on pi_5 of SU(2), revised related discussions and abstract