Geometric Construction of the r-Map: From Affine Special Real to Special Kahler Manifolds

被引：21

作者：

Alekseevsky, D. V. ^{[1
,2
]}

Cortes, V. ^{[3
,4
]}

机构：

[1] Univ Edinburgh, Edinburgh EH9 3JZ, Midlothian, Scotland

[2] JCMB, Maxwell Inst Math Sci, Edinburgh EH9 3JZ, Midlothian, Scotland

[3] Univ Hamburg, Dept Math, D-20146 Hamburg, Germany

[4] Univ Hamburg, Zentrum Math Phys, D-20146 Hamburg, Germany

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2009年 / 291卷 / 02期

关键词：

Manifold; Tangent Bundle; Vector Multiplet; Ricci Curvature; Geometric Construction;

D O I：

10.1007/s00220-009-0803-7

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We give an intrinsic definition of ( affine very) special real manifolds and realise any such manifold M as a domain in affine space equipped with a metric which is the Hessian of a cubic polynomial. We prove that the tangent bundle N = TM carries a canonical structure of ( affine) special Kahler manifold. This gives an intrinsic description of the r-map as the map M -> N = TM. On the physics side, this map corresponds to the dimensional reduction of rigid vector multiplets from 5 to 4 space-time dimensions. We generalise this construction to the case when M is any Hessian manifold.

引用

页码：579 / 590

页数：12