PoS - Proceedings of Science
Volume 430 - The 39th International Symposium on Lattice Field Theory (LATTICE2022) - Vacuum Structure, Confinement, and Chiral Symmetry
SU(N) fractional instantons
J.L. Dasilva Golán* and M. Garcia Perez
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Pre-published on: March 15, 2023
Published on: April 06, 2023
We present our study of a set of solutions to the $SU(N)$ Yang-Mills equations of motion with fractional topological charge. The configurations are obtained numerically by minimizing the action with gradient flow techniques on a torus of size $l^2 \times(Nl)^2$ with twisted boundary conditions. We pay special attention to the large N limit, which is taken along a very peculiar sequence, with the number of colors N and the magnetic flux m selected respectively as the $n$-th and $n − 2$ terms of the Fibonacci sequence. We discuss the large N scaling of the solutions and analyze several gauge invariant quantities as the Polyakov loops. We also discuss the so-called Hamiltonian limit, with one of the large directions sent to infinity, where these instantons represent tunneling events between inequivalent pure gauge configurations.
DOI: https://doi.org/10.22323/1.430.0394
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