Abstract
We consider chiral fermionic conformal field theories constructed from classical error-correcting codes and provide a systematic way of computing their elliptic genera. We exploit the U(1) current of the \( \mathcal{N} \) = 2 superconformal algebra to obtain the U(1)-graded partition function that is invariant under the modular transformation and the spectral flow. We demonstrate our method by constructing extremal \( \mathcal{N} \) = 2 elliptic genera from classical codes for relatively small central charges. Also, we give near-extremal elliptic genera and decompose them into \( \mathcal{N} \) = 2 superconformal characters.
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Acknowledgments
We are grateful to Hee-Cheol Kim, Minsung Kim, and Yutaka Matsuo for their valuable discussions. The work of K. K. and S. Y. was supported by FoPM, WINGS Program, the University of Tokyo. The work of K. K. was supported by JSPS KAKENHI Grant-in-Aid for JSPS fellows Grant No. 23KJ0436.
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Kawabata, K., Yahagi, S. Elliptic genera from classical error-correcting codes. J. High Energ. Phys. 2024, 130 (2024). https://doi.org/10.1007/JHEP01(2024)130
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DOI: https://doi.org/10.1007/JHEP01(2024)130