Random matrices and holographic tensor models

• Published in: The journal of high energy physics Vol. 2017; no. 6; pp. 1 - 26
• Main Authors: Krishnan, Chethan, Kumar, K. V. Pavan, Sanyal, Sambuddha
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2017; Springer Nature B.V; SpringerOpen
• Subjects: 1/N Expansion; Black Holes in String Theory; Classical and Quantum Gravitation; Density of states; Elementary Particles; High energy physics; Holography and condensed matter physics (AdS/CMT); Matrices (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Spectra; String Theory; Symmetry; Black Holes in String Theory; Holography and condensed matter physics (AdS/CMT); 1/N Expansion
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP06(2017)036

A bstract We further explore the connection between holographic O ( n ) tensor models and random matrices. First, we consider the simplest non-trivial uncolored tensor model and show that the results for the density of states, level spacing and spectral form factor are qualitatively identical to the colored case studied in arXiv:1612.06330. We also explain an overall 16-fold degeneracy by identifying various symmetries, some of which were unavailable in SYK and the colored models. Secondly, and perhaps more interestingly, we systematically identify the Spectral Mirror Symmetry and the Time-Reversal Symmetry of both the colored and uncolored models for all values of n , and use them to identify the Andreev ensembles that control their random matrix behavior. We find that the ensembles that arise exhibit a refined version of Bott periodicity in n .