Since strings are one-dimensional objects, they have richer dynamics than point particles. There are many indications that this richness can be captured by a "double field theory", which is a field theory in a double-dimensional space. One of the stringy features that suggests this are winding states: modes where strings have a quantized wrapping number around compact cycles of the space, the simplest yet rich case being that of a circle. Winding modes have a mass proportional to the radius of the circle, while momentum states have a mass proportional to the inverse of the radius. There is a symmetry (T-duality) that interchanges these states while inverting the size of the circle. These two modes are nothing else than the harmonics of the doubled space. However, in order to make the double field theory consistent, a constraint is imposed, such that fields are independent of the T-dual coordinates, and no winding modes are allowed.
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