Abstract
We construct, following [1, 2], a massive M2-brane (supermembrane) as the limit of a genus two M2-brane that becomes a twice punctured Riemann surface with particular boundary conditions on the fields defined on the punctures. The target space is M9 × LCD, where LCD is a genus one light cone diagram. It contains mass terms and a topological term associated with the non-triviality of the target surface that, at low energies, can be associated with the presence of a cosmological constant. We show that the supergravity background of the M2-brane considered in this formulation requires the presence of M9-branes acting as sources. They correspond to the 11D uplift of the characteristic D8’s of Romans supergravity. To this end, we explicitly show that some of the background singularities of the massive M2-brane can be reproduced by the M9-branes found by [3]. This establishes a relation between the Romans mass and the moduli of the massive M2-brane.
When dimensionally reduced, we obtain a worldsheet Hamiltonian of a N=2 type IIA closed superstring in 10D. We denote it massive string. The corresponding massive string inherits a non-vanishing constant term from the topological massive M2-brane that shifts the Hamiltonian. The non-vanishing parameter is related to the non-trivial structure of the massive M2-brane background and it can be related to the Romans mass term. It also contains a modified tension due to the non-trivial dependence on the moduli and on the punctures associated with the target torus.
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Acknowledgments
P.L. has been supported by the projects MINEDUC-UA ANT1956, ANT2156 and ANT2255 of the U. de Antofagasta. P.L. is grateful with ANID/ POSTDOCTORADO BECAS CHILE/ 2022 — 74220031. MPGM is partially supported by the PID2021-125700NB-C21 MCI Spanish Grant. MPGM thanks to the Physics Department at Antofagasta U. for kind hospitality during the research stay, where part of this work was done. P.L. was supported in part by a grant from the Gluskin She /Onex Freeman Dyson Chair in Theoretical Physics and by Perimeter Institute. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Industry Canada and by the Province of Ontario through the Ministry of Colleges and Universities.
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Garcia del Moral, M.P., León, P. & Restuccia, A. Worldsheet description of a massive type IIA superstring in 10D. J. High Energ. Phys. 2023, 104 (2023). https://doi.org/10.1007/JHEP11(2023)104
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DOI: https://doi.org/10.1007/JHEP11(2023)104