T-duality

T-duality (string propagating around a large circular extra dimension = string propagating around a small circular extra dimension)

Properties such as momentum and winding number are swapped moving from one description to the other.

T-duality, will consider strings propagating around the geometry of different extra curricular dimensions and show them to be equivalent. Strings propagating on spacetime geometries of different sizes can be physcially equivalent.

Let’s say you have two different circular extra dimensions. One with the radius: r, and one with the radius: 1/r. Now, let’s say that there are strings that are propagating along these differing geometries. The string will have two properties as it does so:

Momentum, as it propagates along this extra curricular dimension.
Winding number, the number of times the strings winds counterclockwise around this circular extra dimension.

In T-duality, these properties will be identified with each other, in differing string pictures. In other words: momentum and winding number will be swapped moving from the first string picture to the second.

Type IIA and Type IIB string theory are related to each other by T-duality and Heterotic SO (32) and Heterotic E 8 x E 8 are also related to each other by T-duality.

T-duality is another kind of relationship that can exist between string theories. Here we have to consider strings propagating on some kind of circular extra dimension, such as a cylinder. These strings can either be wrapped or unwrapped. The number of times that the string wraps around this circular dimension is known as the winding number. In T-duality, large circular radiuses of these extra dimensions, each have their own corresponding smaller circular radius extra dimension. They are equivalent descriptions. It should be noted, however, that moving from one geometric description to the other, the momentum and winding number of the string is swapped. Type IIA and type IIB string theory are related by T-duality. Both flavors of heterotic string theory are also related to each other by T-duality.

Google Sites

Report abuse