Buscher

Buscher is a surname of German origin. It may refer to people bearing the name, as well as to a set of theoretical physics rules used in string theory. The variant spelling Büscher is sometimes seen in German contexts.

In theoretical physics, the Buscher rules (or Buscher transformations) describe how the background fields of a string propagating in a space with an abelian isometry transform under T-duality. If the target space has a U(1) isometry along a coordinate x, the dual background is obtained by exchanging certain components of the spacetime metric, the antisymmetric B-field, and the dilaton with specific prescriptions. The dual metric and B-field are constructed by inverting the metric component along the isometry and mixing it with the B-field; the remaining components are adjusted accordingly. The dilaton also shifts, ensuring the conformal invariance of the dual theory at the quantum level. A central consequence is that a string theory on a circle of radius R is equivalent to a theory on a circle of radius α′/R, with momentum and winding modes interchanged.

History and impact: The transformation rules were derived by the German physicist Buscher in 1987 and have since become a standard tool for exploring T-duality, generating dual backgrounds, and understanding mirror symmetry in string theory. Generalizations exist for non-abelian isometries and have found applications in cosmology, brane constructions, and duality networks. See also T-duality and string theory.