Revisiting SU(N) integrals
Résumé
In this note, I revisit integrals over $\text{SU}(N)$ of the form ${\int}^{}DU\,{{U}_{{{i}_{1}}\,{{j}_{1}}}}\cdots {{U}_{{{i}_{p}}\,{{j}_{p}}}}U_{{{k}_{1}}{{l}_{1}}}^{\dagger}\cdots U_{{{k}_{n}}{{l}_{n}}}^{\dagger}$ . While the case p = n is well known, it seems that explicit expressions for p = n + N had not appeared in the literature. Similarities and differences, in particular in the large N limit, between the two cases are discussed.