Supersymmetry of IIA warped flux AdS and flat backgrounds

Abstract

Abstract: We identify the fractions of supersymmetry preserved by the most general warped flux AdS and flat backgrounds in both massive and standard IIA supergravities. We find that AdS n × w M 10 − n preserve 2 n/2 k for n ≤ 4 and 2 [n/2]+1 k for 4 < n ≤ 7 supersymmetries, k ∈ 0. In addition we show that, for suitably restricted fields and M 10 − n, the killing spinors of AdS backgrounds are given in terms of the zero modes of Dirac like operators on M 10 − n. This generalizes the Lichnerowicz theorem for connections whose holonomy is included in a general linear group. We also adapt our results to ℝ 1,n − 1 × w M 10 − n backgrounds which underpin flux compactifications to ℝ 1,n − 1 and show that these preserve 2 n/2 k for 2 n+1/2 k for 4 < n ≤ 8, and n2 k for n = 9, 10 supersymmetries.