On the large N limit of matrix integrals over the orthogonal group

Jean-Bernard Zuber (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

We reexamine the large N limit of matrix integrals over the orthogonal group O(N) and their relation with those pertaining to the unitary group U(N). We prove that lim_{N to infty} N^{-2} \int DO exp N tr JO is half the corresponding function in U(N), and a similar relation for lim_{N to infty} \int DO exp N tr(A O B O^t), for A and B both symmetric or both skew symmetric.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Autre [cond-mat.other]; Physique des Hautes Energies - Théorie [hep-th]

Jean-Bernard Zuber. On the large N limit of matrix integrals over the orthogonal group. Journal of Physics A: Mathematical and Theoretical, 2008, 41, pp.382001. ⟨hal-00319243⟩