The spectrum of permutation orbifolds


We study the spectrum of permutation orbifolds of 2d CFTs. We find examples where the light spectrum grows faster than Hagedorn, which is different from known cases such as symmetric orbifolds. We also describe how to compute their partition functions using a generalization of Hecke operators.

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    Note that for finite central charge, there will never be any Hagedorn transition, since asymptotically the growth of states is always given by Cardy growth. Equation 1.1 and similar expressions are understood to hold in the infinite central charge limit, where the partition function can indeed have finite radius of convergence. For finite c having a ‘Hagedorn transition’ simply means that the free energy will scale with c in that regime.


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This work is partly based on the master thesis of one of us (BJM). CAK thanks the Harvard University High Energy Theory Group for hospitality. This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation Grant PHY-1607611. CAK is supported by the Swiss National Science Foundation through the NCCR SwissMAP.

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Correspondence to Christoph A. Keller.

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Keller, C.A., Mühlmann, B.J. The spectrum of permutation orbifolds. Lett Math Phys 109, 1559–1572 (2019).

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  • Conformal field theory
  • Holography
  • Orbifolds
  • Permutation groups

Mathematics Subject Classification

  • 17B69
  • 81T40
  • 05A16