Abstract
We propose a covariant technique to excavate physical bosonic string states by entire trajectories rather than individually. The approach is based on Howe duality: the string’s spacetime Lorentz algebra commutes with a certain inductive limit of sp(•), with the Virasoro constraints forming a subalgebra of the Howe dual algebra sp(•). There are then infinitely many simple trajectories of states, which are lowest-weight representations of sp(•) and hence of the Virasoro algebra. Deeper trajectories are recurrences of the simple ones and can be probed by suitable trajectory-shifting operators built out of the Howe dual algebra generators. We illustrate the formalism with a number of subleading trajectories and compute a sample of tree-level amplitudes.
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Acknowledgments
We would like to thank Thomas Basile, Lucile Cangemi, Paolo Di Vecchia, Maxim Grigoriev, Euihun Joung, Axel Kleinschmidt, Renann Lipinski Jusinskas, Pouria Mazloumi, Oliver Schlotterer, Stephan Stieberger, Stefan Theisen and Arkady Tseytlin for very fruitful discussions and correspondence. We would also like to thank Oliver Schlotterer for very useful comments on an earlier version of the paper. E.S. is Research Associate of the Fund for Scientific Research (FNRS), Belgium. The work of C.M. and E.S. was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 101002551) and by the Fonds de la Recherche Scientifique — FNRS under Grant No. F.4544.21. Both C.M. and E.S. would like to thank the Nordita Institute and program “Amplifying Gravity at All Scales” for hospitality while this work was in progress, where also part of our results were presented by C.M.
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ArXiv ePrint: 2309.15988
Research Associate of the Fund for Scientific Research — FNRS, Belgium. On leave from: Lebedev Institute of Physics. (Evgeny Skvortsov)
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Markou, C., Skvortsov, E. An excursion into the string spectrum. J. High Energ. Phys. 2023, 55 (2023). https://doi.org/10.1007/JHEP12(2023)055
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DOI: https://doi.org/10.1007/JHEP12(2023)055