T-Duality in the Green-Schwarz Formalism, and the Massless/Massive IIA Duality Map

摘要

We derive a component-field expansion of the Green-Schwarz action for thetype IIA string, in an arbitrary background of massless NS-NS and R-R bosonicfields, up to quadratic order in the fermionic coordinates \theta. Using thisaction, we extend the usual derivation of Buscher T-duality rules to includenot only NS-NS, but also R-R fields. Our implementation of the T-dualitytransformation rules makes use of adapted background-field parametrizations,which provide a more geometrically natural and elegant description for theduality maps than the ones previously presented. These T-duality rules allow usto derive the Green-Schwarz action for the type IIB string in an arbitrarybackground of massless NS-NS and R-R bosonic fields, up to O(\theta^2).Implemention of another T-duality transformation on this type IIB action thenallows us also to derive the Green-Schwarz action for the massive IIA string.By further considering T-duality transformations for backgrounds with the twoU(1) isometries of a 2-torus, we give a string-theoretic derivation of thedirect T-duality relation between the massless and massive type IIA strings. Inaddition, we give an explicit construction of the D=8 SL(3,R)xSL(2,R) invariantsupergravity with two mass parameters that form a doublet under the SL(2,R)factor.