# From geometry to non-geometry via T-duality

Research paper by Branislav Sazdovic

Indexed on: 06 Jun '16Published on: 06 Jun '16Published in: High Energy Physics - Theory

#### Abstract

Reconsideration of T-duality of the open string allows us to introduce some geometric features in non-geometric theories. Starting with the observation that general coordinate transformations are T-dual to the gauge transformations, we introduce new, up to now missing term, with additional gauge field $A^D_i$ (D denotes components with Dirichlet boundary conditions). It compensate non-fulfilment of the invariance under general coordinate transformation on the end-points of open string, as well as standard gauge field $A^N_a$ (N denotes components with Neumann boundary conditions) compensate non-fulfilment of the gauge invariance. Using generalized procedure we will perform T-duality of vector fields linear in coordinates. We show that gauge fields $A^N_a$ and $A^D_i$ 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 derivative 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 T-dual field strength invariant. Therefore, we introduce some new features of non-geometric theories where field strength has both antisymmetric and symmetric parts.