T-duality

introduction

the T stands for toroidal
This refers to the situation where one string theory compactified on a circle of radius R, and another string theory compactified on circle of radius 1/R describe the same physics. Therefore when one of the theories is on a very small circle the other theory is on a very large circle.
\(\int \partial X \bar{\partial}X\)
\(X=X+2\pi R\)
T-duality

\[\tilde{R}=\frac{\alpha'}{R}\]