SU(N) fractional instantons and the Fibonacci sequence

Abstract

Abstract We study, by means of numerical methods, new SU(N) self-dual instanton solutions on R × T 3 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 Z N fluxes piercing the box are taken within the Fibonacci sequence, i.e. N = F n (the nth number in the series) and m → $$ \left|\overrightarrow{m}\right| $$ = k → $$ \left|\overrightarrow{k}\right| $$ = F n−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.

Keywords

• 1/N Expansion
• Solitons Monopoles and Instantons
• Vacuum Structure and Confinement
• Lattice Quantum Field Theory