Abstract
Constructing a holographic string theory dual for a CFT in the perturbative, weakly coupled regime is a holy grail for gauge/string dualities that would not only open the door for proofs of the AdS/CFT correspondence but could also provide novel examples of string duals with and without supersymmetry. In this work we consider some marginal perturbation of a family of symmetric product orbifolds in two dimensions. From their correlation functions we engineer a bosonic string theory whose amplitudes are shown to reproduce the CFT correlation function order-by-order both in the coupling and in 1/N. Our derivation does not require to compute and compare correlation functions explicitly but rather relies on a sequence of identities that can be derived using path integral methods. The bosonic string theory we engineer is based on the field content of the Kac-Wakimoto representation of strings in AdS3 with k units of pure NSNS flux, but the interaction terms we obtain are different. They include current algebra preserving interaction terms with one unit of spectral flow.
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Acknowledgments
We wish to thank Federico Ambrosino, Till Bargheer, Lorentz Eberhardt, Bob Knighton, Sean Seed, Alessandro Sfondrini, Vit Sriprachyakul, Yu-ki Suzuki, Joerg Teschner, Takashi Tsuda and Edward Witten for interesting discussions and comments. Thanks also to Bob Knighton, Sean Seet and Vit Sriprachyakul for sharing a preliminary version of their upcoming paper [21]. The work of Y. H. is supported by JSPS Grant-in-Aid for Scientific Research (B) No. 23H01170 and JSPS Grant-in-Aid for Transformative Research Areas (A) No. 21H05187. This project also received funding from the German Research Foundation DFG under Germany’s Excellence Strategy - EXC 2121 Quantum Universe - 39083330.
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Hikida, Y., Schomerus, V. Engineering perturbative string duals for symmetric product orbifold CFTs. J. High Energ. Phys. 2024, 71 (2024). https://doi.org/10.1007/JHEP06(2024)071
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DOI: https://doi.org/10.1007/JHEP06(2024)071