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

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

Luu, Martin. ‘Local Langlands Duality and a Duality of Conformal Field Theories’. arXiv:1506.00663 [hep-Th, Physics:math-Ph], 1 June 2015. http://arxiv.org/abs/1506.00663.
Mathai, Varghese, and Guo Chuan Thiang. ‘T-Duality and Topological Insulators’. arXiv:1503.01206 [hep-Th, Physics:math-Ph], 3 March 2015. http://arxiv.org/abs/1503.01206.