GENERALIZED LIE TRANSPORTED STRING IN T-FOLD WITH GENERALIZED KILLING VECTOR

After constructing the -brane background, which is a T-fold in string theory, from a D7-brane via U-duality, we derived the fundamental string solution rotating around it. Reflecting that the background is not axisymmetric, the string solution also changes its shape during its rotation. However, we found that the background is indeed axisymmetric in the sense of doubled geometry, by explicitly finding a generalized Killing vector. Moreover, the string charge density vector is found to be generalized Lie transported along the generalized Killing vector.