Worldsheet instanton corrections to five-branes and waves in double field theory

Abstract

We make a comprehensive study on the string 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. We discuss a physical interpretation of the winding coordinate dependence. The analysis based on the geometric structures behind the solutions leads to an interpretation of the winding dependence as string worldsheet instanton corrections. We also give a brief discussion on the origins of these winding corrections in gauged linear sigma model. Our analysis reveals that for every supergravity solution, one has DFT solutions that include string winding corrections.

Isometries of five-branes and T-duality

“…In [10] taking into account world-sheet instanton corrections was shown to localize the smeared NS5-brane back to the original one, and localize the KK5-monopole in the directioñ z dual to the special isometry direction. In [11,12] the same has been shown for the 5 2 2brane, whose background acquires dependence on two dual coordinates. Hence, one naturally arrives at description of brane backgrounds in terms of doubled geometry [16,17,19].…”

“…To cure this, one considers world-volume instanton corrections, which localize the smeared NS5-brane back into the full brane background. Special transverse isometry directions were shown to get localized in the corresponding dual space [10][11][12].…”

Exotic branes from del Pezzo surfaces

“…At order α = 2, we obtain the NS5 backgrounds [5 0 2 A/B], the KK-monopoles [5 1 2 A/B], as well as three other non-geometric backgrounds. Their existence has already been argued for -they correspond to the 1-exotic branes completing the T-duality orbit [9,19]. The non-geometric backgrounds found at order α = 3, 4, 5 capture all 1-exotic branes known in the literature [16,18].…”

World-volume effective theories of locally non-geometric branes

“…Therefore, one can perform the formal (non-isometric) T-duality transformation to obtain geometries that are not solutions to supergravity. The 5 3 2 -brane is one of such kind of solution in DFT [22,23]. Due to the absence of the isometries, the 5 3 2 -brane geometry contains the dual coordinatẽ x-dependence.…”

“…They are also classified into the locally non-geometric objects. A remarkable fact is that the localized KK-monopole and the localized Q5-brane are shown to be solutions to DFT [23]. The geometry with the winding corrections are necessary to understand a stringy nature of space-time and it is also discussed in other places [33,34].…”