Abstract
We study an analogue of the Drinfel’d double for algebroids associated with the O(D, D + n) gauged double field theory (DFT). We show that algebroids defined by the twisted C-bracket in the gauged DFT are built out of a direct sum of three (twisted) Lie algebroids. They exhibit a “tripled”, which we call the extended double, rather than the “doubled” structure appearing in (ungauged) DFT. We find that the compatibilities of the extended doubled structure result not only in the strong constraint but also the additional condition in the gauged DFT. We establish a geometrical implementation of these structures in a (2D + n)-dimensional product manifold and examine the relations to the generalized geometry for heterotic string theories and non-Abelian gauge symmetries in DFT.
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Acknowledgments
We are grateful to Jeong-Hyuck Park, Yuho Sakatani and Rui Sun for useful comments on algebroids and integrability during the CQUeST-APCTP Workshop “Gravity beyond Riemannian Paradigm”. The authors would like to express their sincere gratitude to the reviewers for their valuable feedback and insightful comments on this manuscript. Their meticulous review process has greatly contributed to improving the quality and accuracy of the paper. The work of S.S. is supported in part by Grant-in-Aid for Scientific Research (C), JSPS KAKENHI Grant Number JP20K03952. The work of H.M. is supported by Grant-in-Aid for JSPS Research Fellow, JSPS KAKENHI Grant Numbers JP22J14419 and JP22KJ2651.
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Mori, H., Sasaki, S. Extended doubled structures of algebroids for gauged double field theory. J. High Energ. Phys. 2024, 96 (2024). https://doi.org/10.1007/JHEP06(2024)096
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DOI: https://doi.org/10.1007/JHEP06(2024)096