arXiv:0809.0707v1 [math.DG] 3 Sep 2008 CCNV Spacetimes and (Super)symmetries A. Coley 1 , D. McNutt 1 , N. Pelavas 1 1 Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5 aac, ddmcnutt, pelavas@mathstat.dal.ca September 3, 2008 Abstract It is of interest to study supergravity solutions preserving a non- minimal fraction of supersymmetries. A necessary condition for super- symmetry to be preserved is that the spacetime admits a Killing spinor and hence a null or timelike Killing vector. Spacetimes admitting a covariantly constant null vector (CCNV ), and hence a null Killing vector, belong to the Kundt class. We investigate the existence of ad- ditional isometries in the class of higher-dimensional CCNV Kundt metrics. 1 Introduction Supersymmetric supergravity solutions are of interest in the context of the AdS/CFT conjecture, the microscopic properties of black hole entropy, and in a search for a deeper understanding of string theory dualities. For example, in five dimensions solutions preserving various fractions of supersymmetry of N = 2 gauged supergravity have been studied. The Killing spinor equations imply that supersymmetric solutions preserve 2, 4, 6 or 8 of the supersymme- tries. The AdS 5 solution with vanishing gauge field strengths and constant 1