Lectures on Special Kahler Geometry and Electric--Magnetic Duality Rotations
Abstract
In these lectures I review the general structure of electric--magnetic duality rotations in every even space--time dimension. In four dimensions, which is my main concern, I discuss the general issue of symplectic covariance and how it relates to the typical geometric structures involved by N=2 supersymmetry, namely Special K\"ahler geometry for the vector multiplets and either HyperK\"ahler or Quaternionic geometry for the hypermultiplets. I discuss classical continuous dualities versus non--perturbative discrete dualities. How the moduli space geometry of an auxiliary dynamical Riemann surface (or Calabi--Yau threefold) relates to exact space--time dualities is exemplified in detail for the Seiberg Witten model of an gauge theory.
Keywords
Cite
@article{arxiv.hep-th/9512043,
title = {Lectures on Special Kahler Geometry and Electric--Magnetic Duality Rotations},
author = {Pietro Fré},
journal= {arXiv preprint arXiv:hep-th/9512043},
year = {2025}
}
Comments
56 pages, LaTeX, article.sty, espcrc2.sty. Lecture notes at Trieste Spring School 1995