Abstract
Abstract
Double field theory (DFT) is an effective theory of string theory. It has a manifest symmetry of T-duality. The gauge symmetry in DFT is related to some kind of algebroid structures, and they have a doubled structure. We focus on the gauge algebra of the O(D, D+n) gauged DFT and discuss an extension of the doubled structure. The gauge algebra of the O(D, D + n) gauged DFT has been described by the F-bracket. This bracket is related to some algebroid structures. We show that algebroids defined by the twisted C-bracket in the gauged DFT are built out of a direct sum of three Lie algebroids. They exhibit a “triple”, which we call the extended double, rather than a “double” structure. We also consider the geometrical realization of these structures in a (2D + n)-dimensional manifold.
Subject
Computer Science Applications,History,Education
Reference14 articles.
1. Double Field Theory;Hull;J. High Energy Phys.,2009
2. On the geometry of double field theory;Vaisman;J. Math. Phys.,2012
3. Double Field Theory and Membrane Sigma-Models;Chatzistavrakidis;J. High Energy Phys.,2018
4. Doubled Aspects of Vaisman Algebroid and Gauge Symmetry in Double Field Theory;Mori;J. Math. Phys.,2020
5. Hamiltonian structures of lie groups, lie bialgebras and the geometric meaning of the classical Yang-Baxter equation;Drinfel’d;Sov. Math. Dokl.,1983