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On the large D expansion of Hermitian multi-matrix models

par Carrozza, Sylvain;Ferrari, Frank ;Tanasa, Adrian;Valette, Guillaume
Référence Journal of mathematical physics, 61, 7, 073501
Publication Publié, 2020-07-01

Article révisé par les pairs

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Résumé :

We investigate the existence and properties of a double asymptotic expansion in 1/N2 and 1/D in U(N) × O(D) invariant Hermitian multi-matrix models, where the N × N matrices transform in the vector representation of O(D). The crucial point is to prove the existence of an upper bound η(h) on the maximum power D1+η(h) of D that can appear for the contribution at a given order N2-2h in the large N expansion. We conjecture that η(h) = h in a large class of models. In the case of traceless Hermitian matrices with the quartic tetrahedral interaction, we are able to prove that η(h) ≤ 2h; the sharper bound η(h) = h is proven for a complex bipartite version of the model, with no need to impose a tracelessness condition. We also prove that η(h) = h for the Hermitian model with the sextic wheel interaction, again with no need to impose a tracelessness condition.