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Introduction
Introduction
My research lies at the intersection of string theory, generalized geometry, and effective field theory, focusing on understanding the implications of duality symmetries—particularly T-duality and U-duality—on spacetime structure and D-brane dynamics. Central to this pursuit is Double Field Theory, a framework that manifests O($D$, $D$) symmetry by introducing dual coordinates corresponding to winding modes in closed string theory. This approach provides a robust geometric and algebraic structure that captures the extended nature of strings and non-geometric backgrounds beyond conventional supergravity. Studying non-geometric fluxes, such as Q- and R-fluxes, and their embedding into field theories via Double Field Theory provides insight into string compactifications, cosmology, and exotic branes. Furthermore, the development of effective actions for D-branes in Ramond-Ramond background fields—especially the ($p−1$)-form backgrounds—unfolds new gauge symmetries such as volume-preserving diffeomorphisms.
In Double Field Theory, the mass-squared of doubled fields associated with bosonic closed string states is proportional to $N_L+N_R-2$. Massless states are therefore not only the graviton, anti-symmetric, and dilaton fields with ($N_L=1$, $N_R=1$) such theory is focused on, but also the symmetric traceless tensor and the vector field relative to the states ($N_L=2$, $N_R=0$) and ($N_L=0$, $N_R=2$) which are massive in the lower-dimensional non-compactified space. While they are not even physical in the absence of compact dimensions, they provide a sample of states for which both momenta and winding numbers are non-vanishing, differently from the states ($N_L=1$, $N_R=1$). A quadratic action is therefore here built for the corresponding doubled fields. It results that its gauge invariance under the linearized double diffeomorphisms is based on a generalization of the usual weak constraint, giving rise to an extra mass term for the symmetric traceless tensor field, not otherwise detectable: this can be interpreted as a mere stringy effect in target space due to the simultaneous presence of momenta and windings. Furthermore, in the context of the generalized metric formulation, a non-linear extension of the gauge transformations is defined involving the constraint extended from the weak constraint that can be uniquely defined in triple products of fields. Finally, we show that the above mentioned stringy effect does not appear in the case of only one compact doubled space dimension.
Double field theory offers a manifest T-duality formulation for massless closed string field theory with momentum and winding excitations. In this work, we solve and study the properties of Friedmann-Robertson-Walker and doubled spherically symmetric metric of Double Field Theory.
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