# All Science Fair Projects

## Science Fair Project Encyclopedia for Schools!

 Search    Browse    Forum  Coach    Links    Editor    Help    Tell-a-Friend    Encyclopedia    Dictionary

# Science Fair Project Encyclopedia

For information on any area of science that interests you,
enter a keyword (eg. scientific method, molecule, cloud, carbohydrate etc.).
Or else, you can start by choosing any of the categories below.

# T-duality

T-duality is a symmetry of string theory, relating type IIA and type 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 (wrapped twice) will be mapped to a IIB string with two units of momentum, and so on.

The total squared mass of a closed string

$m^2 = \frac{4N}{\alpha'} + \frac{n^2}{R^2} + \frac{w^2R^2}{\alpha^{\prime 2}}$

is invariant under the exchange $R \leftrightarrow \alpha'/R,\quad n\leftrightarrow w$, and the interactions and all other physical phenomena can be proved invariant under this operation, too. T-duality acting on D-branes changes their dimension by +1 or -1.

Andrew Strominger, Shing-Tung Yau, and Eric Zaslow have showed that mirror symmetry can be understood as T-duality applied to three-dimensional toroidal fibres of the Calabi-Yau space.

Also see: S-duality, U-duality, mirror symmetry

03-10-2013 05:06:04