T-duality as coordinates permutation in double space

Abstract

We introduce the $2D$ dimensional double space with the coordinates $Z^M=(x^{\mu },y_{\mu })$ which components are the coordinates of initial space $x^{\mu }$ and its T-dual $y_{\mu }$. We shall show that in this extended space the T-duality transformations can be realized simply by exchanging places of some coordinates $x^a$, along which we want to perform T-duality and the corresponding dual coordinates $y_a$. In such approach it is evident that T-duality leads to the physically equivalent theory and that complete set of T-duality transformations form subgroup of the $2D$ permutation group. So, in the double space we are able to represent the backgrounds of all T-dual theories in unified manner.

To be published in Chinese Physics C

References in corpus (6)

• Double Field Theory
• T-duality and closed string non-commutative (doubled) geometry
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• T-duality as coordinates permutation in double space for weakly curved background
• T-dualization of type II superstring theory in double space
• Fermionic T-duality in fermionic double space

Cited by in corpus (10)

• T-dualization in a curved background in absence of a global symmetry
• T-duality as coordinates permutation in double space for weakly curved background
• T-dualization of type II superstring theory in double space
• Open string T-duality in double space
• Noncommutativity and nonassociativity of closed bosonic string on T-dual toroidal backgrounds
• Fermionic T-duality in fermionic double space
• Courant bracket found out to be T-dual to Roytenberg bracket
• Twisted C-brackets
• Advantage of the second-order formalism in double space T-dualization of type II superstring
• Double space T-dualization and coordinate dependent RR