From geometry to non-geometry via T-duality  

作　　者：B.Sazdovi 

机构地区：[1]Institute of Physics,University of Belgrade

出　　处：《Chinese Physics C》2018年第8期65-87,共23页中国物理C（英文版）

基　　金：Supported by the Serbian Ministry of Education and Science(171031)

摘　　要：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 Ai^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 AaN（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 AaNand AiDare T-dual to ADaand AN^irespectively.We introduce the field strength of T-dual non-geometric theories as derivatives of T-dual gauge fields along both T-dual variable yμand its double？yμ.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.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 Ai^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 AaN（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 AaNand AiDare T-dual to ADaand AN^irespectively.We introduce the field strength of T-dual non-geometric theories as derivatives of T-dual gauge fields along both T-dual variable yμand its double？yμ.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.

关 键 词：T-DUALITY non-geometry open string neumann boundary conditions dirichlet boundary conditions 

分 类 号：O4[理学—物理]