Abstract
With the aim of investigating the existence of an integrable elliptic deformation of strings on AdS3 × S3 × T4, we compute the tree-level worldsheet S-matrix of the elliptically-deformed bosonic sigma model on AdS3 × S3 in uniform light-cone gauge. The resulting tree-level S-matrix is compatible with the integrability of the model and has interesting features, including a hidden U(1) symmetry not manifest in the Lagrangian. We find that it cannot be embedded in the known exact integrable R-matrices describing deformations of the undeformed AdS3 × S3 × T4 light-cone gauge S-matrix including fermions. Therefore, we construct embeddings of the deformed 6-d metric in type II supergravity with constant dilaton and homogeneous fluxes. The simplicity of these solutions suggests they are promising candidates to lead to an integrable string sigma model including fermions.
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Acknowledgments
ALR and FS thank the participants of the Workshop “Integrability in Low Supersymmetry Theories” in Filicudi, Italy for stimulating discussions. We also would like to thank Sergey Frolov for pointing out the connection between the choice of light-cone gauge fixing and JT transformations, Alessandro Torrielli, Davide Polvara and Sylvain Lacroix for discussions, and Sibylle Driezen and Riccardo Borsato for collaboration on a related project. The work of BH and ALR was supported by a UKRI Future Leaders Fellowship (grant number MR/T018909/1). The work of FS was supported by the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement number 101027251.
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Hoare, B., Retore, A.L. & Seibold, F.K. Elliptic deformations of the AdS3 × S3 × T4 string. J. High Energ. Phys. 2024, 42 (2024). https://doi.org/10.1007/JHEP04(2024)042
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DOI: https://doi.org/10.1007/JHEP04(2024)042