Composing arbitrarily many $SU(N)$ fundamentals

Alexios P. Polychronakos; Konstantinos Sfetsos

doi:10.1016/j.nuclphysb.2023.116314

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arXiv · 2305.19345

Composing arbitrarily many $SU(N)$ fundamentals

Alexios P. Polychronakos·Konstantinos Sfetsos

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Abstract

We compute the multiplicity of the irreducible representations in the decomposition of the tensor product of an arbitrary number $n$ of fundamental representations of $SU(N)$, and we identify a duality in the representation content of this decomposition. Our method utilizes the mapping of the representations of $SU(N)$ to the states of free fermions on the circle, and can be viewed as a random walk on a multidimensional lattice. We also derive the large-$n$ limit and the response of the system to an external non-abelian magnetic field. These results can be used to study the phase properties of non-abelian ferromagnets and to take various scaling limits.

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Alexios P. Polychronakos, Konstantinos Sfetsos. 2023-05-30. Composing arbitrarily many $SU(N)$ fundamentals. https://doi.org/10.1016/j.nuclphysb.2023.116314

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