Vaisman Algebroid and Doubled Structure of Gauge Symmetry in Double Field Theory

Abstract

The Vaisman algebroid is a kind of algebroid structure. It is de ned by an extension of the Courant algebroid, and phisically related to the gauge symmetry in Double Field Theory (DFT), which is an effective theory of string theory. DFT has T-duality as a manifest symmetry. In this study, we focus on the \doubled structure” in the Vaisman algebroid. It is already well known that some kind of Lie algebras are obtained by the Drinfel’d double of Lie bialgebras. The Courant algebroid is obtaind by the Drinfel’d double of Lie bialgebroids. We nd that the Vaisman algebroid can be obtained by an analogue of the \Drinfel’d double” of Lie algebroids. We discuss the algebraic origin of the strong constraint in DFT.