Using the Exact Renormalisation Group with the Local Potential Approximation, it is claimed that in d=4 space-time dimensions we may avoid the usual triviality problem of O(N) scalar fields using non-quantised eigen-perturbations around the Gaussian fixed point, called the Halpern-Huang directions. We re-derive these directions and show that they do not have the correct scaling properties and have non-universal properties. By expanding the Halpern-Huang directions in quantised perturbations we conclude that the usual quantised-perturbations span the entire theory space, proving the triviality of O(N) scalar field theory in d=4.
University of Southampton
Thursday, December 4, 2014 - 13:00
Building 46, seminar room (5th floor)
Fate of the Halpern-Huang Relevant Directions in O(N) Scalar Field Theory