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We compute the annulus diagram corresponding to the interaction of a fractional D3 brane with a gauge field on its world-volume and a stack of N fractional D3 branes on the orbifolds C 2 /Z 2 and C 3 /(Z 2 × Z 2 ). We show that its logarithmic divergence can be equivalently understood as due either to massless open string states circulating in the loop or to massless closed string states exchanged between two boundary states. This follows from the fact that, under open/closed string duality, massless states in the open and closed string channels are matched into each other without mixing with massive states. This explains why the perturbative properties of many gauge theories living on the worldvolume of less supersymmetric and nonconformal branes have been recently obtained from their corresponding supergravity solution.

In this paper we review the conditions for the validity of the gauge/gravity correspondence in both supersymmetric and nonsupersymmetric string models. We start by reminding what happens in type IIB theory on the orbifolds ℂ2/ℤ2and ℂ3/(ℤ2x ℤ2), where this correspondence beautifully works. In these cases, by performing a complete stringy calculation of the interaction among D3-branes, it has been shown that the fact that this correspondence works is a consequence of the open/closed duality and of the absence of threshold corrections. Then we review the construction of type 0 theories with their orbifolds and orientifolds having spectra free from both open and closed string tachyons and for such models we study the validity of the gauge/gravity correspondence, concluding that this is not a peculiarity of supersymmetric theories, but it may work also for nonsupersymmetric models. Also in these cases, when it works, it is again a consequence of the open/closed string duality and of vanishing threshold corrections.

We discuss two inequivalent ways for describing magnetized D-branes wrapped N times on a torus T 2 . The first one is based on a non-abelian gauge bundle U (N ), while the second one is obtained by means of a Narain T-duality transformation acting on a theory with non-magnetized branes. We construct in both descriptions the boundary state and the open string vertices and show that they give rise to different string amplitudes. In particular, the description based on the gauge bundle has open string vertex operators with momentum dependent Chan-Paton factors.

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 1 Introduction Generalized Geometry (GG) was first introduced by N. J. Hitchin in ref. [1]. As the author himself states in his pedagogical lectures [2], it is based on two premises: the first consists in replacing the tangent bundle T of a manifold M with T ⊕ T * , a bundle with the same base space M but fibers given by the direct sum of tangent and cotangent spaces. The second consists in replacing the Lie bracket on the sections of T , which are vector fields, with the Courant bracket which involves vector fields and one-forms. The construction is then extended to general vector bundles E over M so to have E ⊕ E * and a suitable bracket for the sections of the new bundle.The formal setting of GG has recently attracted the interest of theoretical physicists in relation to Double Field Theory (DFT) [3]. We shall propose in this paper a model whose analysis can help to establish more rigorously a possible bridge between the two through the doubled world-sheet formalism that generates DFT.DFT has emerged as a proposal to incorporate T-duality [4,5], a peculiar symmetry of a compactified string on a d-torus T d in a (G, B)-background, as a manifest symmetry of the string effective field theory. In order to achieve this goal, the action of this field theory has to be generalized in such a way that the emerging carrier space of the dynamics be doubled with