We study the double- and triple-scaling limits of a complex multi-matrix model, with symmetry. The double-scaling limit amounts to taking simultaneously the large- (matrix size) and large- (number of matrices) limits while keeping the ratio fixed. The triple-scaling limit consists in taking the large- limit while tuning the coupling constant to its critical value and keeping fixed the product , for some value of that depends on the particular combinatorial restrictions imposed on the model. Our first main result is the complete recursive characterization of the Feynman graphs of arbitrary genus which survive in the double-scaling limit. Next, we classify all the dominant graphs in the triple-scaling limit, which we find to have a plane binary tree structure with decorations. Their critical behavior belongs to the universality class of branched polymers. Lastly, we classify all the dominant graphs in the triple-scaling limit under the restriction to three-edge connected (or two-particle irreducible) graphs. Their critical behavior falls in the universality class of Liouville quantum gravity (or, in other words, the Brownian sphere).
Publié le :
DOI : 10.4171/aihpd/121
Mots-clés : matrix models, large-N limit, classification and enumeration of graphs
@article{AIHPD_2022__9_2_367_0, author = {Benedetti, Dario and Carrozza, Sylvain and Toriumi, Reiko and Valette, Guillaume}, title = {Multiple scaling limits of $\operatorname{U}(N)^2 \times \operatorname{O}(D)$ multi-matrix models}, journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D}, pages = {367--433}, volume = {9}, number = {2}, year = {2022}, doi = {10.4171/aihpd/121}, mrnumber = {4450018}, zbl = {1513.81110}, language = {en}, url = {http://archive.numdam.org/articles/10.4171/aihpd/121/} }
TY - JOUR AU - Benedetti, Dario AU - Carrozza, Sylvain AU - Toriumi, Reiko AU - Valette, Guillaume TI - Multiple scaling limits of $\operatorname{U}(N)^2 \times \operatorname{O}(D)$ multi-matrix models JO - Annales de l’Institut Henri Poincaré D PY - 2022 SP - 367 EP - 433 VL - 9 IS - 2 UR - http://archive.numdam.org/articles/10.4171/aihpd/121/ DO - 10.4171/aihpd/121 LA - en ID - AIHPD_2022__9_2_367_0 ER -
%0 Journal Article %A Benedetti, Dario %A Carrozza, Sylvain %A Toriumi, Reiko %A Valette, Guillaume %T Multiple scaling limits of $\operatorname{U}(N)^2 \times \operatorname{O}(D)$ multi-matrix models %J Annales de l’Institut Henri Poincaré D %D 2022 %P 367-433 %V 9 %N 2 %U http://archive.numdam.org/articles/10.4171/aihpd/121/ %R 10.4171/aihpd/121 %G en %F AIHPD_2022__9_2_367_0
Benedetti, Dario; Carrozza, Sylvain; Toriumi, Reiko; Valette, Guillaume. Multiple scaling limits of $\operatorname{U}(N)^2 \times \operatorname{O}(D)$ multi-matrix models. Annales de l’Institut Henri Poincaré D, Tome 9 (2022) no. 2, pp. 367-433. doi : 10.4171/aihpd/121. http://archive.numdam.org/articles/10.4171/aihpd/121/
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