Comparing Double String Theory Actions

Understand

Aimed to a deeper comprehension of a manifestly T-dual invariant formulation of string theory, in this paper a detailed comparison between the non-covariant action proposed by Tseytlin and the covariant one proposed by Hull is done.

• These are obtained by making both the string coordinates and their duals explicitly appear, on the same foot, in the world-sheet action, so "doubling" the string coordinates along the compact dimensions.
• After a discussion of the nature of the constraints in both the models and the relative quantization, it results that the string coordinates and their duals behave like "non-commuting" phase space type coordinates but their expressions in terms of Fourier modes generate the oscillator algebra of the standard bosonic string formulation.
• A proof of the equivalence of the two formulations is given.