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

TL;DR

This paper develops a detailed Green-Schwarz formalism for type IIA and IIB strings, extending T-duality rules to include R-R fields, and derives the duality map between massless and massive IIA strings using background field parametrizations.

Contribution

It provides a new geometric formulation of T-duality rules including R-R fields and explicitly constructs the mass parameters in supergravity related to the duality.

Findings

Derived component-field Green-Schwarz action up to quadratic order in fermions.

Extended T-duality rules to include R-R fields with geometric parametrizations.

Established the T-duality map between massless and massive IIA strings.

Abstract

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 \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). Implemention 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)xSL(2,R) invariant supergravity with two mass parameters that form a doublet under the SL(2,R) factor.