Geometric Low-Energy Effective Action in a Doubled Spacetime

The ten-dimensional supergravity theory is a geometric low-energy effective theory and the equations of motion for its fields can be obtained from string theory by computing $\beta$ functions. With $d$ compact dimensions, we can add to it an $O(d, d;\mathbb{Z})$ geometric structure and construct the supergravity theory inspired by double field theory through the use of a suitable commutative star product. The latter implements the weak constraint of the double field theory on its fields and gauge parameters in order to have a closed gauge symmetry algebra. The consistency of the action here proposed is based on the orthogonality of the momenta associated with fields in their triple star products in the cubic terms defined for $d\ge1$. This orthogonality holds also for an arbitrary number of star products of fields for $d=1$. Finally, we extend our analysis to the double sigma model, non-commutative geometry and open string theory.Comment: 27 pages, minor changes, references adde

T-Dualities and Doubled Geometry of the Principal Chiral Model

The Principal Chiral Model (PCM) defined on the group manifold of SU(2) is here investigated with the aim of getting a further deepening of its relation with Generalized and Doubled Geometry. A one-parameter family of equivalent Hamiltonian descriptions is introduced, and cast into the form of Born geometries. Then O(3,3) duality transformations of the target phase space are performed and we show that the resulting dual models are defined on the group SB(2,C) which is the Poisson-Lie dual of SU(2) in the Iwasawa decomposition of the Drinfel'd double SL(2, C). Moreover, starting from the Lagrangian approach, a new kind of duality is found between the SU(2) PCM and the natural one defined on SB(2,C) which is not an isometry of the target phase space. A parent action with doubled degrees of freedom and configuration space SL(2, C) is then defined that reduces to either one of the dually related models, once suitable constraints are implemented.Comment: 41 pages, revised version published in JHE

Principal Chiral Model without and with WZ term: Symmetries and Poisson-Lie T-Duality

Duality properties of the $SU(2)$ Principal Chiral Model are investigated starting from a one-parameter family of its equivalent Hamiltonian descriptions generated by a non-Abelian deformation of the cotangent space $T^*SU(2) \simeq SU(2) \ltimes \mathbb{R}^3$. The corresponding dual models are obtained through $O(3,3)$ duality transformations and result to be defined on the group $SB(2,\mathbb{C})$, which is the Poisson-Lie dual of $SU(2)$ in the Iwasawa decomposition of the Drinfel'd double $SL(2,\mathbb{C})=SU(2) \bowtie SB(2,\mathbb{C})$.These dual models provide an explicit realization of Poisson-Lie T-duality. A doubled generalized parent action is then built on the tangent space $TSL(2,\mathbb{C})$. Furthermore, a generalization of the $SU(2)$ PCM with a WZ term is shortly discussed.Comment: 25 pages, Contribution to the Proceedings of Corfu Summer Institute 2019 "Schools and Workshops on Elementary Particle Physics and Gravity

Boundary State for Magnetized D9 Branes and One-Loop Calculation

We construct the boundary state describing magnetized D9 branes in R^{3,1} x T^6 and we use it to compute the annulus and Moebius amplitudes. We derive from them, by using open/closed string duality, the number of Landau levels on the torus T^d.Comment: 12 pages,in honor of Adriano Di Giacomo on his 70th birthday, contribution to the Festschrif

On off-shell bosonic string amplitudes

We give a simple prescription for computing, in the framework of the bosonic string theory, off-shell one-loop amplitudes with any number of external massless particles, both for the open and for the closed string. We discuss their properties and, in particular, for the two-string one-loop amplitudes we show their being transverse.Comment: 12 pages, Latex. One reference added. Introduction and conclusions expanded. Some other minor changes in the tex

Jacobi sigma models

We introduce a two-dimensional sigma model on surfaces with boundary and target space a Jacobi manifold. The model yields a topological open string theory. In the Hamiltonian approach first class constraints are derived, which generate gauge invariance of the model under diffeomorphisms. By introducing a metric term, a non-topological sigma model is obtained, yielding a Polyakov action with metric and B-field, whose target space is a Jacobi manifold.Comment: 21 pages. Latex2e. Minor changes, references adde

Doubling, T-Duality and Generalized Geometry: a Simple Model

A simple mechanical system, the three-dimensional isotropic rigid rotator, is here investigated as a 0+1 field theory, aiming at further investigating the relation between Generalized/Double Geometry on the one hand and Doubled World-Sheet Formalism/Double Field Theory, on the other hand. The model is defined over the group manifold of SU(2) and a dual model is introduced having the Poisson-Lie dual of SU(2) as configuration space. A generalized action with configuration space SL(2,C), i.e. the Drinfel'd double of the group SU(2), is then defined: it reduces to the original action of the rotator or to its dual, once constraints are implemented. The new action contains twice as many variables as the original. Moreover, its geometric structures can be understood in terms of Generalized Geometry. keywords: Generalized Geometry, Double Field Theory, T-Duality, Poisson-Lie symmetry.Comment: 37 pages. Revised version to appear in JHE