# T-duality

**T-duality** is a symmetry of

M-theory, relating IIA and IIB string theory, and the two heterotic string theories. T-duality transformations act on spaces in which at least one direction has the topology of a circle. Under the transformation, the radius R of that direction will be changed to 1/R, and "wrapped" string states will be exchanged with high-momentum string states in the dual theory.

For example, one might begin with a IIA string wrapped once around the direction in question. Under T-duality, it will be mapped to a IIB string which has momentum in that direction. A IIA string with a winding number of two (i.e., wrapped twice) will be mapped to a IIB string with two units of momentum, and so on.

**Also see**: S-duality, U-duality