Geometric Algebra Techniques in Flux Compactifications
Elena Mirela Babalic (Horia Hulubei National Institute for Physics and Nuclear Engineering, Department of Theoretical Physics, Strada Reactorului No. 30, P.O. BOX MG-6, 077125 Magurele, Romania); Calin Iuliu Lazaroiu (Institute for Basic Science, Center for Geometry and Physics, Pohang 790-784, Republic of Korea); Ioana Alexandra Coman (DESY, Theory Group, Notkestrasse 85, Building 2a, 22607 Hamburg, Germany)
We study “constrained generalized Killing (s)pinors,” which characterize supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually clear and computationally effective methods for translating supersymmetry conditions into differential and algebraic constraints on collections of differential forms. In particular, we give a synthetic description of Fierz identities, which are an important ingredient of such problems. As an application, we show how our approach can be used to efficiently treat compactification of M-theory on eight manifolds and prove that we recover results previously obtained in the literature.
