SU(N) fractional instantons and the Fibonacci sequence

Abstract

We study, by means of numerical methods, new SU(N) self-dual instanton solutions on R × T3 with fractional topological charge Q = 1/N. They are obtained on a box with twisted boundary conditions with a very particular choice of twist: both the number of colours and the ’t Hooft ZN fluxes piercing the box are taken within the Fibonacci sequence, i.e. N = Fn (the nth number in the series) and left|overrightarrow{m}right| = left|overrightarrow{k}right| = Fn−2. Various arguments based on previous works and in particular on ref. [1], indicate that this choice of twist avoids the breakdown of volume independence in the large N limit. These solutions become relevant on a Hamiltonian formulation of the gauge theory, where they represent vacuum-to-vacuum tunneling events lifting the degeneracy between electric flux sectors present in perturbation theory. We discuss the large N scaling properties of the solutions and evaluate various gauge invariant quantities like the action density or Wilson and Polyakov loop operators.