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    Permutations and the combinatorics of gauge invariants for general N 
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    Permutations and the combinatorics of gauge invariants for general N

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    arXiv (785.4Kb)
    Publisher
    SISSA
    Journal
    Proceedings of Science
    ISSN
    1824-8039
    Metadata
    Show full item record
    Abstract
    Group algebras of permutations have proved highly useful in solving a number of problems in large N gauge theories. I review the use of permutations in classifying gauge invariants in one-matrix and multi-matrix models and computing their correlators. These methods are also applicable to tensor models and have revealed a link between tensor models and the counting of branched covers. The key idea is to parametrize $U(N)$ gauge invariants using permutations, subject to equivalences. Correlators are related to group theoretic properties of these equivalence classes. Fourier transformation on symmetric groups by means of representation theory offers nice bases of functions on these equivalence classes. This has applications in AdS/CFT in identifying CFT duals of giant gravitons and their perturbations. It has also lead to general results on quiver gauge theory correlators, uncovering links to two dimensional topological field theory and the combinatorics of trace monoids.
    Authors
    Ramgoolam, S
    URI
    http://qmro.qmul.ac.uk/xmlui/handle/123456789/12488
    Collections
    • Physics and Astronomy [1178]
    Licence information
    http://arxiv.org/abs/1605.00843
    Copyright statements
    © Copyright owned by the author(s)
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