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Pablo Diaz Benito
순수물리이론 연구단
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Invariant operators, orthogonal bases and correlators in general tensor models

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Title
Invariant operators, orthogonal bases and correlators in general tensor models
Author(s)
Pablo Diaz; Soo-Jong Rey
Publication Date
2018-07
Journal
NUCLEAR PHYSICS B, v.932, no., pp.254 - 277
Publisher
ELSEVIER SCIENCE BV
Abstract
We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models of (gauge) symmetry Gd=U(N1)⊗⋯⊗U(Nd). As a continuation and completion of our earlier work, we present two natural ways of counting invariants, one for arbitrary Gd and another valid for large rank of Gd. We construct bases of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite rank of Gd diagonalizes the two-point function of the free theory. It is analogous to the restricted Schur basis used in matrix models. We show that the constructions get almost identical as we swap the Littlewood–Richardson numbers in multi-matrix models with Kronecker coefficients in general tensor models. We explore the parallelism between matrix model and tensor model in depth from the perspective of representation theory and comment on several ideas for future investigation. © 2018 The Authors
URI
https://pr.ibs.re.kr/handle/8788114/4946
ISSN
0550-3213
Appears in Collections:
Center for Fundamental Theory(순수물리이론 연구단) > Journal Papers (저널논문)
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