Cardoso, Gabriel Lopes and Mohaupt, Thomas 
ORCID: 0000-0002-6864-4086
(2020)
Special Geometry, Hessian Structures and Applications.
Physics Reports, 855.
pp. 1-141.
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Abstract
The target space geometry of abelian vector multiplets in ${\cal N}= 2$ theories in four and five space-time dimensions is called special geometry. It can be elegantly formulated in terms of Hessian geometry. In this review, we introduce Hessian geometry, focussing on aspects that are relevant for the special geometries of four- and five-dimensional vector multiplets. We formulate ${\cal N}= 2$ theories in terms of Hessian structures and give various concrete applications of Hessian geometry, ranging from static BPS black holes in four and five space-time dimensions to topological string theory, emphasizing the role of the Hesse potential. We also discuss the r-map and c-map which relate the special geometries of vector multiplets to each other and to hypermultiplet geometries. By including time-like dimensional reductions, we obtain theories in Euclidean signature, where the scalar target spaces carry para-complex versions of special geometry.
| Item Type: | Article |
|---|---|
| Additional Information: | Invited review article, prepared for submission to Phys. Rept., 196 p. plus appendices and reference (87 p.). v2: references added. v3: minor changes. Discussion of centroaffine hypersurfaces added, references added |
| Uncontrolled Keywords: | hep-th, hep-th, math-ph, math.DG, math.MP |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 03 Mar 2020 09:33 |
| Last Modified: | 18 Jan 2023 23:59 |
| DOI: | 10.1016/j.physrep.2020.02.002 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3077186 |
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