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The Level Two and Three Modular Invariants of SU (n)

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Abstract

In this Letter, we explicitly classify all modular invariant partition functions for \(A_r^{(1)} \) at levels 2 and 3. Previously, these were known only for level 1. Level 2 exceptions exist at r=9, 15, and 27;level 3 exceptions exist at r=4, 8, and 20. One of these is new, but the others were all anticipated by the ‘rank-level duality’ relating \(A_r^{(1)} \) level k and \(A_{k - 1}^{(1)} \) level r+1. The main recent result which this Letter rests on is the classification of ‘\(\mathcal{A}\mathcal{D}\mathcal{E}_7 \)-type invariants’.

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References

  1. Cappelli, A., Itzykson, C. and Zuber, J.-B.: Comm. Math. Phys. 113(1987), 1–26.

    Google Scholar 

  2. Gannon, T.: Comm. Math. Phys. 161(1994), 233–264.

    Google Scholar 

  3. Degiovanni, P.: Comm. Math. Phys. 127(1990), 71–99.

    Google Scholar 

  4. Gannon, T.: Nuclear Phys. B 396(1993), 708–736.

    Google Scholar 

  5. Gannon, T.: Kac–Peterson, Perron–Frobenius, and the classification of conformal field theories, 1995, q-alg/9510026.

  6. Kac, V. G.: Infinite Dimensional Lie Algebras, 3rd edn, Cambridge University Press, Cambridge, 1990.

    Google Scholar 

  7. Schellekens, A. N. and Yankielowicz, S.: Phys. Lett. B 227(1989), 387–391.

    Google Scholar 

  8. Walton, M. A.: Nuclear Phys. B 322(1989), 775–790.

    Google Scholar 

  9. Verstegen, D.: Nuclear Phys. B 346(1990), 349–386.

    Google Scholar 

  10. Font, A.: Modern Phys. Lett. A 6(1991), 3265–3272.

    Google Scholar 

  11. Altschuler, D., Bauer, M. and Itzykson, C.: Comm. Math. Phys. 161(1994), 233–264.

    Google Scholar 

  12. Gannon, T.: The classification of SU(3) modular invariants revisited, to appear in Ann. IHP, Phys. Théor., hep-th/9404185.

  13. Coste, A. and Gannon, T.: Phys. Lett. B 323(1994), 316–321.

    Google Scholar 

  14. Ruelle, Ph., Thiran, E. and Weyers, J.: Nuclear Phys. B 402(1993), 693–708.

    Google Scholar 

  15. Aoki, N.: Amer. J. Math. 113(1991), 779–833.

    Google Scholar 

Download references

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  1. Max-Planck-Institut für Mathematik, Gottfried-Claven-Strasse 26, D-53225, Bonn, Germany

    TERRY GANNON

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  1. TERRY GANNON
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GANNON, T. The Level Two and Three Modular Invariants of SU (n). Letters in Mathematical Physics 39, 289–298 (1997). https://doi.org/10.1023/A:1007369013693

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