Abstract
We study T-duality with non-zero components of NSNS two form field along directions we dualize with the help of canonical formalism. As a result of this procedure we determine generalized Buscher’s rules. We also apply the same procedure to the case of non-relativistic string.
Highlights
We study T-duality with non-zero components of NSNS two form field along directions we dualize with the help of canonical formalism
NSNS two form are multiplied with world-sheet antisymmetric symbol while expressions with target space metric are multiplied with world-sheet metric so that it is very difficult to solve them
We show that generally under T-duality non-relativistic string maps to the relativistic one with specific form of the background fields and we analyze conditions that determine that non-relativistic string maps to non-relativistic string again
Summary
T-duality with non-trivial NSNS two form along directions we dualize is remarkably complex if we consider general bosonic string. As the last important step we introduced matric Hmn defined as Hmn = Gmn − BmM GMN BNm. In order to determine transformation rules for metric and NSNS two form field under these T-duality transformations we have to find Lagrangian for T-dual string. Bmn = GmkBklGln , Bμν = Bμν + GμmGmnBnν − BμmGmnGnν + BμmGmnBnlGlkBkν + GμkGklBlmGmnGnν , Bμ n = [Gμm − BμkGklBlm]Gmn , Gmn[Gnμ These are most general T-duality transformation rules in case of non-zero components of NSNS two form along directions where T-duality is performed. Bαβ introduced on the last line in (2.19) are pullbacks of T-dual components of metric and NSNS two form given in (2.21) to the string’s world-sheet. We focus on T-duality with non-zero NSNS two form in case of nonrelativistic string
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