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A Hurwitz theory avatar of open–closed strings

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Abstract

We review and explain an infinite-dimensional counterpart of the Hurwitz theory realization (Alexeevski and Natanzon, Math. Russ. Izv. 72:3–24, 2008) of algebraic open–closed-string model à la Moore and Lazaroiu, where the closed and open sectors are represented by conjugation classes of permutations and the pairs of permutations, i.e. by the algebra of Young diagrams and bipartite graphs, respectively. An intriguing feature of this Hurwitz string model is the coexistence of two different multiplications, reflecting the deep interrelation between the theory of symmetric and linear groups, S ∞ and GL(∞).

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Notes

  1. Note that originally the CF algebra was defined for finite-dimensional algebras. The subtlety of the infinite-dimensional case is discussed in [11, 12].

References

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Acknowledgements

S.N. is grateful to MPIM for the kind hospitality and support.

Our work is partly supported by Ministry of Education and Science of the Russian Federation under contract 2012-1.5-12-000-1003-009, by Russian Federation Government Grant No. 2010-220-01-077, by the National Research University Higher School of Economics’ Academic Fund Program in 2013-2014 (research grant No. 12-01-0122), by NSh-3349.2012.2 (A.Mir. and A.Mor.) and 8462.2010.1 (S.N.), by RFBR grants 10-02-00509 (A.Mir. and S.N.), 10-02-00499 (A.Mor.) and by joint grants 11-02-90453-Ukr, 12-02-91000-ANF, 12-02-92108-Yaf-a, 11-01-92612-Royal Society.

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Authors and Affiliations

  1. Lebedev Physics Institute, Moscow, Russia

    A. Mironov

  2. ITEP, Moscow, Russia

    A. Mironov, A. Morozov & S. Natanzon

  3. Department of Mathematics, Higher School of Economics, Moscow, Russia

    S. Natanzon

  4. A.N. Belozersky Institute, Moscow State University, Moscow, Russia

    S. Natanzon

Authors
  1. A. Mironov
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  2. A. Morozov
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  3. S. Natanzon
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Correspondence to A. Mironov.

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Mironov, A., Morozov, A. & Natanzon, S. A Hurwitz theory avatar of open–closed strings. Eur. Phys. J. C 73, 2324 (2013). https://doi.org/10.1140/epjc/s10052-013-2324-y

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  • DOI: https://doi.org/10.1140/epjc/s10052-013-2324-y

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