Permutation centralizer algebras and multimatrix invariants Article Swipe
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· 2016
· Open Access
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· DOI: https://doi.org/10.1103/physrevd.93.065040
· OA: W2271820369
We introduce a class of permutation centralizer algebras which underly the\ncombinatorics of multi-matrix gauge invariant observables. One family of such\nnon-commutative algebras is parametrised by two integers. Its Wedderburn-Artin\ndecomposition explains the counting of restricted Schur operators, which were\nintroduced in the physics literature to describe open strings attached to giant\ngravitons and were subsequently used to diagonalize the Gaussian inner product\nfor gauge invariants of 2-matrix models. The structure of the algebra, notably\nits dimension, its centre and its maximally commuting sub-algebra, is related\nto Littlewood-Richardson numbers for composing Young diagrams. It gives a\nprecise characterization of the minimal set of charges needed to distinguish\narbitrary matrix gauge invariants, which are related to enhanced symmetries in\ngauge theory. The algebra also gives a star product for matrix invariants. The\ncentre of the algebra allows efficient computation of a sector of multi-matrix\ncorrelators. These generate the counting of a certain class of bi-coloured\nribbon graphs with arbitrary genus.\n
