From geometry to non-geometry via T-duality

Abstract

Reconsideration of the T-duality of the open string allows us to introduce some geometric features in non-geometric theories. First, we have found what symmetry is T-dual to the local gauge transformations. It includes transformations of background fields but does not include transformations of the coordinates. According to this we have introduced a new, up to now missing term, with additional gauge field $A_i^D$ (D denotes components with Dirichlet boundary conditions). It compensates non-fulfilment of the invariance under such transformations on the end-points of an open string, and the standard gauge field $A_a^N$ (N denotes components with Neumann boundary conditions) compensates non-fulfilment of the gauge invariance. Using a generalized procedure we will perform T-duality of vector fields linear in coordinates. We show that gauge fields $A_a^N$ and $A_i^D$ are T-dual to ${}^{\star }{A}_D^a$ and ${}^{\star }{A}_N^i$ respectively. We introduce the field strength of T-dual non-geometric theories as derivatives of T-dual gauge fields along both T-dual variable $y_{\mu }$ and its double ${\tilde{y}}_{\mu }$. This definition allows us to obtain gauge transformation of non-geometric theories which leaves the T-dual field strength invariant. Therefore, we introduce some new features of non-geometric theories where field strength has both antisymmetric and symmetric parts. This allows us to define new kinds of truly non-geometric theories.

44 pages, To be published in Chinese Physics C

References in corpus (8)

• Double Field Theory
• Symmetry, Gravity and Noncommutativity
• T-duality and closed string non-commutative (doubled) geometry
• D-Branes, RR-Fields and Duality on Noncommutative Manifolds
• Sigma models for genuinely non-geometric backgrounds
• T-dualization in a curved background in absence of a global symmetry
• T-duality as coordinates permutation in double space for weakly curved background
• Open string T-duality in double space

Cited by in corpus (3)

• Open string T-duality in double space
• Open-string T-duality and applications to non-geometric backgrounds
• Courant bracket found out to be T-dual to Roytenberg bracket