On G/H Geometry and Its Use in M-Theory Compactifications

✍ Scribed by Leonardo Castellani

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 127 KB
• Volume: 287
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.2000.6097

✦ Synopsis

The Riemannian geometry of coset spaces is reviewed, with emphasis on its applications to supergravity and M-theory compactifications. Formulae for the connection and curvature of rescaled coset manifolds are generalized to the case of nondiagonal Killing metrics. The example of the N 010 spaces is discussed in detail. These are a subclass of the coset manifolds N pqr =GÂH=SU(3)_U( 1)ÂU( 1)_U(1), the integers p, q, r characterizing the embedding of H in G. We study the realization of N 010 as GÂH=SU(3)_SU( 2)ÂU( 1)_SU(2) (with diagonal embedding of the SU( 2) # H into G). For a particular G-symmetric rescaling there exist three Killing spinors, implying N=3 supersymmetry in the AdS 4 _N 010 compactification of D=11 supergravity. This rescaled N 010 space is of particular interest for the AdS 4 ÂCFT 3 correspondence, and its SU(3)_SU(2) isometric realization is essential for the OSp(4 | 3) classification of the Kaluza Klein modes.