The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders

• Verfasst von: Gurǎu, Rǎzvan [VerfasserIn]
• Titel: The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
• Verf.angabe: Razvan Gurau
• E-Jahr: 2012
• Jahr: 3 August 2012
• Umfang: 15 S.
• Fussnoten: Gesehen am 05.10.2022
• Titel Quelle: Enthalten in: Nuclear physics <Amsterdam> / B
• Ort Quelle: Amsterdam : North-Holland Publ. Co., 1967
• Jahr Quelle: 2012
• Band/Heft Quelle: 865(2012), 1, Seite 133-147
• ISSN Quelle: 1873-1562
• DOI: doi:10.1016/j.nuclphysb.2012.07.028
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Critical behavior
• Sach-SW: expansion
• Sach-SW: Random tensor models
• K10plus-PPN: 180517651X

Abstract

Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson equations, generalizing the loop equations of matrix models, translate into constraints satisfied by the partition function. The constraints have been shown, in the large N limit, to close a Lie algebra indexed by colored rooted D-ary trees yielding a first generalization of the Virasoro algebra in arbitrary dimensions. In this paper we complete the Schwinger Dyson equations and the associated algebra at all orders in 1/N. The full algebra of constraints is indexed by D-colored graphs, and the leading order D-ary tree algebra is a Lie subalgebra of the full constraints algebra.