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New algebraic structures from Hermitian one-matrix model

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Abstract

Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field Theory (CFT) method. From multi-loop equations of the one-matrix model, we get a more general constraint. It can be expressed in terms of the operator algebras, which is the Virasoro subalgebra with extra parameters. In this sense, we named as generalized Virasoro constraint. We enlarge this algebra with central extension, this is a new kind of algebra, and the usual Virasoro algebra is its subalgebra. And we give a bosonic realization of its subalgebra.

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Acknowledgements

The authors would like to thank the Kavli Institute for Theoretical Physics China at the Chinese Academy of Sciences, where part of the work was done in the period of the program entitled “MathematicalMethods from Physics” hold at July 22–Sep. 5, 2013.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Xiang Mao Ding, Yu Ping Li & Ling Xian Meng

  2. College of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, 450002, P. R. China

    Ling Xian Meng

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  1. Xiang Mao Ding
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  2. Yu Ping Li
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Correspondence to Xiang Mao Ding.

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Ding, X.M., Li, Y.P. & Meng, L.X. New algebraic structures from Hermitian one-matrix model. Acta. Math. Sin.-English Ser. 33, 1193–1205 (2017). https://doi.org/10.1007/s10114-017-6268-2

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  • DOI: https://doi.org/10.1007/s10114-017-6268-2

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