T-duality in the Green–Schwarz formalism, and the massless/massive IIA duality map Original Research Article

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 bosonic fields, up to quadratic order in the fermionic coordinates θ. 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(θ2). 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)×SL(2,R) invariant supergravity with two mass parameters that form a doublet under the SL(2,R) factor.