Buscher procedure

The Buscher procedure derives T-dual backgrounds by replacing the derivative of an isometric target coordinate with an independent worldsheet one-form and imposing its flatness with a Lagrange multiplier. Integrating out either field yields the original or dual sigma model.

The Buscher rules invert the metric component along an Abelian isometry and transform the other metric and B-field components. The Gaussian functional determinant also shifts the dilaton; when the metric is block diagonal with $G_{zz}=V$, $\tilde{\Phi }=\Phi -\frac{1}{2}\log V$.