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Rényi entropy of single-character CFTs on the torus

Luis Alberto León Andonayre1,* and Rahul Poddar2,†

  • *Contact author: lal10@hi.is
  • †Contact author: rahul.poddar@unf.edu
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Phys. Rev. D 112, 025011 – Published 15 July, 2025

DOI: https://doi.org/10.1103/qt5p-sl5f

Abstract

We introduce a nonperturbative approach to calculate the Rényi entropy of a single interval on the torus for single-character (meromorphic) conformal field theories. Our prescription uses the Wrońskian method of Mathur, Mukhi, and Sen [Nucl. Phys. B312, 15 (1989)], in which we construct differential equations for torus conformal blocks of the twist two-point function. As an illustrative example, we provide a detailed calculation of the second Rényi entropy for the E8,1 Wess-Zumino-Witten (WZW) model. We find that the Z2 cyclic orbifold of a meromorphic conformal field theory (CFT) results in a four-character CFT, which realizes the toric code modular tensor category. The Z2 cyclic orbifold of the E8,1 WZW model, however, yields a three-character CFT since two of the characters coincide. We then compute the torus conformal blocks and find that the twist two-point function, and therefore the Rényi entropy, is two-periodic along each cycle of the torus. The second Rényi entropy for a single interval of the E8,1 WZW model has the universal logarithmic divergent behavior in the decompactification limit of the torus, as expected as well as the interval approaches the size of the cycle of the torus. Furthermore, we see that the q-expansion is UV finite, apart from the leading universal logarithmic divergence. We also find that there is a divergence as the size of the entangling interval approaches the cycle of the torus, suggesting that gluing two tori along an interval the size of a cycle is a singular limit.

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Phys. Rev. D 112, 025011– Published 15 July, 2025
  • Received 19 December 2024
  • Accepted 17 June 2025
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