# Geometry, Gravity and Supersymmetry

24-28 April 2017
Mainz Institute for Theoretical Physics, Johannes Gutenberg University
Europe/Berlin timezone

## The ASK/PSK-correspondence and the r-map

26 Apr 2017, 10:15
30m
02.430 (Mainz Institute for Theoretical Physics, Johannes Gutenberg University)

### 02.430

#### Mainz Institute for Theoretical Physics, Johannes Gutenberg University

Staudingerweg 9 / 2nd floor, 55128 Mainz

### Speaker

Mr Peter-Simon Dieterich (Universität Hamburg)

### Description

We formulate a correspondence between affine and projective special Kähler manifolds of the same dimension. As an application, we show that, under this correspondence, the affine special Kähler manifolds in the image of the rigid r-map are mapped to one-parameter deformations of projective special Kähler manifolds in the image of the supergravity r-map. The above one-parameter deformations are interpreted as perturbative $\alpha'$-corrections in heterotic and type-II string compactifications with $N=2$ supersymmetry. We show that the completeness of the deformed supergravity r-map metric depends solely on the (well-understood) completeness of the undeformed metric and the sign of the deformation parameter.

### Primary authors

Mr Peter-Simon Dieterich (Universität Hamburg) Prof. Thomas Mohaupt (University of Liverpool) Prof. Vicente Cortés (Department of Mathematics, University of Hamburg)

### Presentation Materials

 Slides
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