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 Kähler geometry for the vector multiplets and either HyperKähler 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 $SU(2)$ gauge theory.

56 pages, LaTeX, article.sty, espcrc2.sty. Lecture notes at Trieste Spring School 1995

References in corpus (5)

• Simple Singularities and N=2 Supersymmetric Yang-Mills Theory
• The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory
• Duality Transformations in Supersymmetric Yang-Mills Theories coupled to Supergravity,
• Gauged Hyperinstantons and Monopole Equations
• On the Monodromies of N=2 Supersymmetric Yang-Mills Theory

Cited by in corpus (25)

• N=2 Supergravity and N=2 Super Yang-Mills Theory on General Scalar Manifolds: Symplectic Covariance, Gaugings and the Momentum Map
• Black Holes and Solitons in String Theory
• Non-Semisimple Gaugings of D=5 N=8 Supergravity and FDA.s
• N=4 Superconformal Mechanics and the Potential Structure of AdS Spaces
• Higgs branch, HyperKahler quotient and duality in SUSY N=2 Yang-Mills theories
• N=8 supersymmetric mechanics on special Kähler manifolds
• Shadow multiplets in AdS_4/CFT_3 and the super-Higgs mechanism: hints of new shadow supergravities
• Superstring Orientifolds with Torsion: O5 Orientifolds of Torus Fibrations and their Massless Spectra
• N=8 BPS Black Holes with 1/2 or 1/4 Supersymmetry and Solvable Lie Algebra Decompositions
• Elements of (super-)Hamiltonian Formalism
• Theory of Superdualities and the Orthosymplectic Supergroup
• Topics in Cubic Special Geometry
• Symplectic Gravity Models in Four, Three and Two Dimensions
• Symplectic covariance of the N=2 hypermultiplets
• The many symmetries of Calabi-Yau compactifications
• The $c$-map, Tits Satake subalgebras and the search for $\mathcal{N}=2$ inflaton potentials
• N = 1, D = 6 Supergravity: Duality and non Minimal Couplings
• A construction of G_2 holonomy spaces with torus symmetry
• The Complete Form of N=2 Supergravity and its Place in the General Framework of D=4 N--Extended Supergravities
• Duality invariance in Fayet-Iliopoulos gauged supergravity
• Construction of projective special Kähler manifolds
• Symmetries of deformed supersymmetric mechanics on Kähler manifolds
• Toric hyperkahler manifolds with quaternionic Kahler bases and supergravity solutions
• Partial Breaking in Rigid Limit of $\mathcal{N}=2$ Gauged Supergravity
• Geometry and integrability in $\mathcal{N}=8$ supersymmetric mechanics