Non-holomorphic Deformations of Special Geometry and Their Applications

G.C. Lopes Cardoso, B. de Wit, S. Mahapatra

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

Abstract

The aim of these lecture notes is to give a pedagogical introduction to the subject of non-holomorphic deformations of special geometry. This subject was first introduced in the context of N = 2 BPS black holes, but has a wider range of applicability. A theorem is presented according to which an arbitrary point-particle Lagrangian can be formulated in terms of a complex function F, whose features are analogous to those of the holomorphic function of special geometry. A crucial role is played by a symplectic vector that represents a complexification of the canonical variables, i.e. the coordinates and canonical momenta.We illustrate the characteristic features of the theorem in the context of field theory models with duality invariances. The function F may depend on a number of external parameters that are not subject to duality transformations.We introduce duality covariant complex variables whose transformation rules under duality are independent of these parameters. We express the real Hesse potential of N = 2 supergravity in terms of the new variables and expand it in powers of the external parameters. Then we relate this expansion to the one encountered in topological string theory. These lecture notes include exercises which are meant as a guidance to the reader.
Original languageEnglish
Title of host publicationBlack Objects in Supergravity
EditorsS. Bellucci
Place of PublicationCham
PublisherSpringer
Pages1-58
Number of pages358
ISBN (Print)978-3-319-00214-9
DOIs
Publication statusPublished - 2013

Publication series

NameSpringer proceedings in physics
Number144

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