In double field theory, the T-duality transformation of exchangingmomentum andwinding modes of closed strings ontoroidal backgrounds translates to a generalized coordinate transformation on a doubledspacetime, where one set of its coordinates is dual to momentum modes and the second set of coordinates is interpreted as dual to winding modes of the closed string. Whether the second set of coordinates has physical meaning depends on how the level-matching condition of closed strings is implemented in the theory: either through the weak constraint or the strong constraint.[5]
Weakly constrained double field theory, introduced byChris Hull andBarton Zwiebach in 2009, allows for the fields to depend on the whole doubledspacetime and encodes genuine momentum and winding modes of the string.[6] While early constructions were limited to cubic interactions, the formulation was extended to include quartic interactions on toroidal backgrounds in 2023 by Bonezzi, Chiaffrino, Díaz-Jaramillo and Hohm.[7]
In strongly constrained double field theory, which was anticipated byWarren Siegel in 1993, the strong constraint ensures the dependency of the fields on only one set of the doubled coordinates;[8][9] it describes the massless fields of closed string theory, i.e. thegraviton,Kalb Ramond B-field, anddilaton, but does not include any winding modes, and serves as a T-duality invariant reformulation ofsupergravity.
Double field theory has been a setting for studying various string theoretical properties such as: consistent Kaluza-Klein truncations of higher-dimensional supergravity to lower-dimensional theories,[10][11] generalizedfluxes,[12] and alpha-prime corrections of string theory in the context ofcosmology andblack holes.[13]
