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arXiv · 2212.01264

SU(N) fractional Instantons

Jorge Luis Dasilva Golan·Margarita Garcia Perez
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Abstract

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.

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Jorge Luis Dasilva Golan, Margarita Garcia Perez. 2022-12-02. SU(N) fractional Instantons. https://arxiv.org/abs/2212.01264

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