T-duality in the Green-Schwarz formalism, and the massless/massive IIA duality map

We derive a component-field expansion of the Green-Schwarz action for the type IIA string, in an arbitrary background of massless NS-NS and R-R busonic fields, up to quadratic order in the fermionic coordinates theta. Using this action, we extend the usual derivation of Buscher T-duality rules to include not only NS-NS, but also R-R fields. Our implementation of the T-duality transformation rules makes use of adapted background-field parametrizations, which provide a more geometrically natural and elegant description for the duality maps than the ones previously presented. These T-duality rules allow us to derive the Green-Schwarz action for the type IIB string in an arbitrary background of massless NS-NS and R-R bosonic fields, up to O(theta(2)). Implementation of another T-duality transformation on this type IIB action then allows us also to derive the Green-Schwarz action for the massive IIA string. By further considering T-duality transformations for backgrounds with the two U(1) isometries of a 2-torus, we give a string-theoretic derivation of the direct T-duality relation between the massless and massive type IIA strings, In addition, we give an explicit construction of the D = 8 SL(3,R) X SL(2,R) invariant supergravity with two mass parameters that form a doublet under the SL(2,R) factor. (C) 2000 Elsevier. Science B.V. All rights reserved.