Winding Corrected Five-branes in Double Field Theory
We discuss a physical interpretation of the winding coordinate (the Fourier conjugate to the string winding modes) dependence of geometries. We study the winding corrections to supergravity solutions in double field theory (DFT). We find five-brane and wave solutions of diverse codimensions in which the winding coordinates are naturally included. The winding coordinate dependence is interpreted as the string worldsheet instanton corrections. We also give a brief discussion on the origins of these winding corrections in a gauged linear sigma model (GLSM). We propose the "semi-doubled GLSM" that provides a string sigma model whose target spaces are five-branes of codimension two. Moreover, we discuss the winding coordinate dependence from the viewpoint of the worldvolume theories. We construct the worldvolume theory of five-branes by using DFT. For example, in the case of a Kaluza-Klein (KK) monopole, we identify three of the four position moduli as being the position coordinates of center in the physical space while the remaining one corresponds to the center in the winding space. The KK-monopole has the fluctuation to the direction of the winding space. The same discussion is applied to a exotic $5^2_2$-brane. This talk is based on JHEP07(2018)001, JHEP12(2018)095 and research currently in preparation.