Orthogonal bases of invariants in tensor models

• Main Authors: Pablo Diaz, Soo-Jong Rey
• Format: Article
• Language: English
• Published: SpringerOpen 2018-02-01
• Series: Journal of High Energy Physics
• Subjects: Gauge Symmetry; Models of Quantum Gravity; Gauge-gravity correspondence; Matrix Models
• Online Access: http://link.springer.com/article/10.1007/JHEP02(2018)089

Abstract Representation theory provides an efficient framework to count and classify invariants in tensor models of (gauge) symmetry G d = U(N 1) ⊗ · · · ⊗ U(N d ) . We show that there are two natural ways of counting invariants, one for arbitrary G d and another valid for large rank of G d . We construct basis of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite rank of G d diagonalizes two-point function. It is analogous to the restricted Schur basis used in matrix models. We comment on future directions for investigation.