MG14 - Talk detail

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In this talk a review of the manifestly T-dual invariant formulation of bosonic string theory will be given. This can be obtained by making both the usual string compact coordinates and their duals explicitly appear, on the same footing, in the world-sheet action. A "doubling" of the string coordinates along the compact dimensions is therefore implied. A peculiarity of such a model is the loss of the local Lorentz invariance which is required to be recovered on-shell. This requirement dictates a constraint on the backgrounds implying the geometry of the double torus determined by the O(D,D) invariant metric in the case of constant background fields. It is interesting to see that this invariance results to be, therefore, an output of the theory, coming from its consistency. In the first part of the talk arbitrary backgrounds will be considered with the general expression of the equations of motion for the string coordinates, boundary conditions and the general constraint that has to be satisfied for having local Lorentz invariance on-shell. Then their explicit specialization in the case of constant backgrounds will be given. After that, in the cases of non-constant backgrounds, it will be shown how and when the deformation from the O(D,D) invariance can be implied. Results of the quantization of the model will be also exhibited: the string coordinates and their duals behave like non-commuting phase space coordinates but their expressions in terms of Fourier modes generate the oscillator algebra of the standard formulation of the bosonic string.

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