Fermionic T-duality in massive type IIA supergravity on $$AdS_{10-k} \times M_k$$ A d S 10 - k × M k

Ilya Bakhmatov

doi:10.1140/epjc/s10052-016-4004-1

Abstract

Fermionic T-duality transformation is studied for the N=1 supersymmetric solutions of massive type IIA supergravity with the metric AdS_{10-k} x M_k for k=3 and 5. We derive the Killing spinors of these backgrounds and use them as an input for the fermionic T-duality transformation. The resulting dual solutions form a large family of supersymmetric deformations of the original solutions by complex valued RR fluxes. We observe that the Romans mass parameter does not change under fermionic T-duaity, and prove its invariance in the k=3 case.

Highlights

Families of new supersymmetric solutions in type II supergravity of the form Ad S10−k × Mk were found in [1,2,3] for k = 3, 4, 5
In this article we study the effect of fermionic T-duality on the Ad S10−k × Mk solutions for k = 3 and k = 5
The key difference from the ordinary Tduality rules is that the metric and the NSNS 2-form field b do not change, whereas the RR fluxes are transformed in a certain way that depends on the Killing spinors of the original background

Summary

Introduction

The key difference from the ordinary Tduality rules is that the metric and the NSNS 2-form field b do not change, whereas the RR fluxes are transformed in a certain way that depends on the Killing spinors of the original background. In order to construct fermionic T-duals of the solutions of [1,3] we study the unbroken supersymmetries of these backgrounds and solve the Killing spinor equations in full generality. While formally applicable to both ordinary and massive type IIA supergravity, the analysis of [22] assumed vanishing mass parameter m before the duality transformation, and resulted in keeping m zero after the duality as well It was later reported [23] that the extension of the transformation of [22] to a nonzero Romans mass, when applied to characteristic solutions of massive type IIA, such as D8-branes and the warped product Ad S6 × S4 [24], yields no change in the mass parameter, and that the entire transformation is trivial in that case.

Killing spinors

Fermionic T-duality

Constant fermionic T-duality parameter

Constant Romans mass parameter

Discussion