Abstract
We use the new nilpotent formulation of open-closed string field theory to explore the limit where the number N of identical D-branes of the starting background is large. By reformulating the theory in terms of the ’t Hooft coupling λ := κN, where κ is the string coupling constant, we explicitly see that at large N only genus zero vertices with arbitrary number of boundaries survive. After discussing the homotopy structure of the obtained large N open-closed theory we discuss the possibility of integrating out the open string sector with a quantum but planar homotopy transfer. As a result we end up with a classical closed string field theory, described by a weak L∞-algebra containing a tree-level tadpole which, to first order in λ, is given by the initial boundary state. We discuss the possibility of removing the tadpole with a closed string vacuum shift solution, to end up with a new classical closed string background, where the initial D-branes have been turned into pure closed-string backreaction.
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Acknowledgments
We thank Ted Erler, Raghu Mahajan and Yuji Okawa for discussions. We thank the organizers and the participants of the workshop “Matrix Models and String Field Theory”, Benasque, May 2023 for the very stimulating atmosphere where this work has been presented. JV thanks INFN Turin for their hospitality during the initial stages of this work. The work of CM and AR is partially supported by the MUR PRIN contract 2020KR4KN2 String Theory as a bridge between Gauge Theories and Quantum Gravity and by the INFN project ST&FI String Theory and Fundamental Interactions. The work of JV was supported by the NCCR SwissMAP that is funded by the Swiss National Science Foundation.
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Maccaferri, C., Ruffino, A. & Vošmera, J. Open-closed string field theory in the large N limit. J. High Energ. Phys. 2023, 119 (2023). https://doi.org/10.1007/JHEP09(2023)119
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DOI: https://doi.org/10.1007/JHEP09(2023)119