T-duality

T-duality is a symmetry between small and large distances that is not present in Kaluza-Klein compactification of a particle theory. It relates different string theories that everyone thought were completely unrelated before T-duality was understood. T-duality preceded the Second Superstring Revolution. [http://www.superstringtheory.com/experm/exper5a1.html superstringtheory] article "Looking for extra dimensions" by [http://www.superstringtheory.com/author.html Patricia Schwarz] ]

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:$m^2\; =\; frac\{4N\}\{alpha\text{'}\}\; +\; frac\{n^2\}\{R^2\}\; +\; frac\{w^2R^2\}\{alpha^\{prime\; 2$is invariant under the exchange $R\; leftrightarrow\; alpha\text{'}/R,quadnleftrightarrow\; w$, 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.

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See also

*S-duality
*U-duality
*Mirror symmetry
*Dualities in string theory