Lectures on nonlinear sigma-models in projective superspace

Abstract

N = 2 supersymmetry in four space-time dimensions is intimately related to hyperkahler and quaternionic Kahler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkahler manifolds. On the other hand, when coupled to N = 2 supergravity, the sigma-model target spaces must be quaternionic Kahler. It is known that such manifolds of restricted holonomy are difficult to generate explicitly. Projective superspace is a field-theoretic approach to constructing general N = 2 supersymmetric nonlinear sigma-models, and hence to generate new hyperkahler and quaternionic Kahler metrics. Intended for a mixed audience consisting of both physicists and mathematicians, these lectures provide a pedagogical introduction to the projective-superspace approach.

56 pages. Lectures given at the 30th Winter School Geometry and Physics, Srni, Czech Republic, 16--23 January, 2010. V2: typos corrected, comments added; V3: almost published version (quotation from Osip Mandelstam was removed by J. Phys. A from published article)

References in corpus (8)

• 4D N = 2 Supergravity and Projective Superspace
• On conformal supergravity and projective superspace
• On superconformal projective hypermultiplets
• Hyper-Kahler Sigma Models on (Co)tangent Bundles with SO(n) isometry
• Deriving Projective Hyperspace from Harmonic
• Polar supermultiplets, Hermitian symmetric spaces and hyperkahler metrics
• Chiral formulation for hyperkaehler sigma-models on cotangent bundles of symmetric spaces
• New extended superconformal sigma models and Quaternion Kahler manifolds

Cited by in corpus (18)

• On a ${\mathbb{Z}}_2^n$-Graded Version of Supersymmetry
• Extended superconformal higher-spin gauge theories in four dimensions
• A new approach to curved projective superspace
• Mixed three-point functions of conserved currents in three-dimensional superconformal field theory
• New nilpotent $\mathcal{N}=2$ superfields
• The Real Anatomy of Complex Linear Superfields
• Conformal interactions between matter and higher-spin (super)fields
• Minkowski superspaces and superstrings as almost real-complex supermanifolds
• New Fayet-Iliopoulos terms in $\mathcal{N}=2$ supergravity
• On higher-spin $\mathcal{N}=2$ supercurrent multiplets
• Comments on N = 2 supersymmetric sigma models in projective superspace
• Three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
• $\mathcal{N}=2$ super Yang-Mills theory in Projective Superspace
• The Conformal Hyperplet
• Component on-shell actions of supersymmetric 3-branes II. 3-brane in D=8
• One-loop divergences in the six-dimensional $\mathcal{N}=(1,0)$ hypermultiplet self-coupling model
• Supergroup approach to the Hubbard model
• On a structure of the one-loop divergences in $4D,\mathcal{N}=2$ supersymmetric sigma-model