SPECIAL GEOMETRY, CUBIC POLYNOMIALS AND HOMOGENEOUS QUATERNIONIC SPACES

被引:168
作者
DEWIT, B [1 ]
VANPROEYEN, A [1 ]
机构
[1] UNIV LOUVAIN,INST THEORET FYS,B-3001 LOUVAIN,BELGIUM
关键词
D O I
10.1007/BF02097627
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The existing classification of homogeneous quaternionic spaces is not complete. We study these spaces in the context of certain N = 2 supergravity theories, where dimensional reduction induces a mapping between special real, Kahler and quaternionic spaces. The geometry of the real spaces is encoded in cubic polynomials, those of the Kahler and quaternionic manifolds in homogeneous holomorphic functions of second degree. We classify all cubic polynomials that have an invariance group that acts transitively on the real manifold. The corresponding Kahler and quaternionic manifolds are then homogeneous. We find that they lead to a well-defined subset of the normal quaternionic spaces classified by Alekseevskii (and the corresponding special Kahler spaces given by Cecotti), but there is a new class of rank-3 spaces of quaternionic dimension larger than 3. We also point out that some of the rank-4 Alekseevskii spaces were not fully specified and correspond to a finite variety of inequivalent spaces. A simpler version of the equation that underlies the classification of this paper also emerges in the context of W3 algebras.
引用
收藏
页码:307 / 333
页数:27
相关论文
共 39 条
[1]  
Alekseevsky D.V., 1975, MATH USSR IZV, V9, P297
[2]  
Atiyah MF., 1964, TOPOLOGY, V3, P3, DOI [10.1016/0040-9383(64)90003-5, DOI 10.1016/0040-9383(64)90003-5]
[3]   EXTENSIONS OF THE VIRASORO ALGEBRA CONSTRUCTED FROM KAC-MOODY ALGEBRAS USING HIGHER-ORDER CASIMIR INVARIANTS [J].
BAIS, FA ;
BOUWKNEGT, P ;
SURRIDGE, M ;
SCHOUTENS, K .
NUCLEAR PHYSICS B, 1988, 304 (02) :348-370
[4]   COSET CONSTRUCTION FOR EXTENDED VIRASORO ALGEBRAS [J].
BAIS, FA ;
BOUWKNEGT, P ;
SURRIDGE, M ;
SCHOUTENS, K .
NUCLEAR PHYSICS B, 1988, 304 (02) :371-391
[5]   (2,2) VACUUM CONFIGURATIONS FOR TYPE-IIA SUPERSTRINGS - N = 2 SUPERGRAVITY LAGRANGIANS AND ALGEBRAIC-GEOMETRY [J].
BODNER, M ;
CADAVID, AC ;
FERRARA, S .
CLASSICAL AND QUANTUM GRAVITY, 1991, 8 (05) :789-807
[6]   DIMENSIONAL REDUCTION OF TYPE-IIB SUPERGRAVITY AND EXCEPTIONAL QUATERNIONIC MANIFOLDS [J].
BODNER, M ;
CADAVID, AC .
CLASSICAL AND QUANTUM GRAVITY, 1990, 7 (05) :829-845
[7]   A PAIR OF CALABI-YAU MANIFOLDS AS AN EXACTLY SOLUBLE SUPERCONFORMAL THEORY [J].
CANDELAS, P ;
DELAOSSA, XC ;
GREEN, PS ;
PARKES, L .
NUCLEAR PHYSICS B, 1991, 359 (01) :21-74
[8]   SPECIAL KAHLER GEOMETRY - AN INTRINSIC FORMULATION FROM N=2 SPACE-TIME SUPERSYMMETRY [J].
CASTELLANI, L ;
DAURIA, R ;
FERRARA, S .
PHYSICS LETTERS B, 1990, 241 (01) :57-62
[9]   SPECIAL GEOMETRY WITHOUT SPECIAL COORDINATES [J].
CASTELLANI, L ;
DAURIA, R ;
FERRARA, S .
CLASSICAL AND QUANTUM GRAVITY, 1990, 7 (10) :1767-1790
[10]   HOMOGENEOUS KAHLER-MANIFOLDS AND T-ALGEBRAS IN N = 2 SUPERGRAVITY AND SUPERSTRINGS [J].
CECOTTI, S .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1989, 124 (01) :23-55