2012/12/31 by Calin-Iuliu Lazaroiu, Calin Iuliu Lazaroiu, Elena-Mirela Babalic +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic number #Algorithm #Black Holes and Theoretical Physics #Compactification (mathematics) #Computer science #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Supergravity #Supersymmetry #Theoretical physics #hep-th #math.DG
paper · pdf · doi:10.1155/2016/7292534
published as Adv. High Energy Phys. 2016, 7292534 · 70 pages
openalex publication_date 2016/01/01 · arxiv created 2016/02/21 · openalex created_date 2016/06/24 · arxiv updated 2016/11/08 · openalex updated_date 2026/08/05
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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>compactification of M -theory on eight manifolds and prove that we recover results previously obtained in the literature.