Eigenvalue method for multi-matrix invariants

Tuesday 30 Jul 2024, 17:30 → 18:30 Asia/Tokyo

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Date: July 30th (Tue), 17:30 (JST)
Speaker: Ryo Suzuki (Shing-Tung Yau Center of Southeast University)
Title: Eigenvalue method for multi-matrix invariants

Abstract: Multi-matrix invariants, or equivalently the scalar multi-trace operators of N=4 super Yang-Mills with U(N) gauge symmetry, are in one-to-one correspondence with the elements of the permutation centralizer algebra (PCA), which is a generalisation of the symmetric group algebra. We develop a new method to explicitly construct all the irreducible representations of PCA up to a modest value of the operator length. The main idea is to consider the eigensystem of the commuting subalgebras of PCA, and to identify the eigenvectors with the orthonormal bases of operators of N=4 SYM, known as the restricted Schur basis and covariant basis. Furthermore, we find that all the coefficients of these operator bases, or equivalently eigenvector elements, can be integer.
This talk is based on arXiv:2408.nnnnn, done in collaboration with S. Ramgoolam (QMUL) and Adrian Padellaro (Bielefeld).