Abstract
\( T\overline{T} \) deformed conformal field theories can be reformulated as worldsheet theories of non-critical strings. We use this correspondence to compute and study the \( T\overline{T} \) deformed partition sum of a symmetric product CFT. We find that it takes the form of a partition sum of a second quantized string theory with a worldsheet given by the product of the seed CFT and a gaussian sigma model with the two-torus as target space. We show that deformed symmetric product theory admits a natural UV completion that exhibits a strong weak coupling ℤ2 duality that interchanges the momentum and winding numbers and maps the \( T\overline{T} \)-coupling λ to its inverse 1/λ. The ℤ2 duality is part of a full O(2, 2, ℤ)-duality group that includes a PSL(2, ℤ) acting on the complexified \( T\overline{T} \) coupling. The duality symmetry eliminates the appearance of complex energies at strong coupling for all seed CFTs with central charge c ≤ 6.
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Acknowledgments
We thank Shazia-Ayn Babul, Cyuan-Han Chang, Liam Fitzpatrick, Shota Komatsu, Alexander Maloney, and Erik Verlinde for very valuable discussions. The research of NB is supported by the Sherman Fairchild Foundation and the U.S. Department of Energy, Office of Science, Office of High Energy Physics Award Number DE-SC0011632. The research of SC is supported by the Sam B. Treiman fellowship at the Princeton Center for Theoretical Science. The research of HV is supported by NSF grant PHY-2209997. JK is supported by NSF grant PHY-2207584.
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Benjamin, N., Collier, S., Kruthoff, J. et al. S-duality in \( T\overline{T} \)-deformed CFT. J. High Energ. Phys. 2023, 140 (2023). https://doi.org/10.1007/JHEP05(2023)140
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DOI: https://doi.org/10.1007/JHEP05(2023)140