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.
Winding modes were introduced in the formalism for the first time in  (IPhT, University of Buenos Aires and Centro Atomico Bariloche) where it was shown that the double field theory action precisely reproduces the string theory scattering amplitudes for strings on a circle of radius close to one (in string units). This realises a perfect identification between the string and double field theory results in the regime where certain string states become massless.
 G. Aldazabal, M. Graña, S. Iguri, M. Mayo, C. Nuñez and J. A. Rosabal, "Enhanced gauge symmetry and winding modes in Double Field Theory'', arXiv:1510.07644 [hep-th], JHEP, DOI 10.1007/JHEP03(2016)093