Quaternionic metrics from harmonic superspace : lagrangian approach and quotient construction

Abstract

Starting from the most general harmonic superspace action of self-interacting Q^+ hypermultiplets in the background of N=2 conformal supergravity, we derive the general action for the bosonic sigma model with a generic 4n dimensional quaternionic-Kahler (QK) manifold as the target space. The action is determined by the analytic harmonic QK potential. We find out this action to have two flat limits. One gives the hyper-Kahler sigma model with a 4n dimensional target manifold, while another yields a conformally invariant sigma model with 4(n+1) dimensional hyper-Kahler target. We work out the harmonic superspace version of the QK quotient construction and use it to give a new derivation of QK extensions of Taub-NUT and Eguchi-Hanson metrics. We analyze in detail the geometrical and symmetry structure of the second metric. The QK sigma model approach allows us to reveal the enhancement of its isometry group to SU(3) or SU(2,1) at the special relations between its parameters : the Einstein constant and the "mass".

34 pages, Latex2e, no figures

References in corpus (5)

• Hyper-Kahler manifolds and multiply-intersecting branes
• Cones, Tri-Sasakian Structures and Superconformal Invariance
• Rigid N=2 superconformal hypermultiplets
• U-duality Twists and Possible Phase Transitions in 2+1D Supergravity
• Quaternionic Taub-NUT from the harmonic space approach

Cited by in corpus (21)

• On superconformal projective hypermultiplets
• Solvable Models of Domain Walls in N=1 Supergravity
• Conformal properties of hypermultiplet actions in six dimensions
• Massive Nonlinear Sigma Models and BPS Domain Walls in Harmonic Superspace
• Gauge Fields, Nonlinear Realizations, Supersymmetry
• Summing up D-instantons in N=2 supergravity
• U(1) x U(1) Quaternionic Metrics from Harmonic Superspace
• Wall Solution with Weak Gravity Limit in Five Dimensional Supergravity
• Harmonicity in N=4 supersymmetry and its quantum anomaly
• BPS Multi-Walls in Five-Dimensional Supergravity
• On conformal supergravity and harmonic superspace
• N=4 supersymmetric Eguchi-Hanson sigma model in d=1
• Computing the Scalar Field Couplings in 6D Supergravity
• A New Class of N=2 Topological Amplitudes
• Quaternionic Extension of the Double Taub-NUT Metric
• Harmonic Superspace, Minimal Unitary Representations and Quasiconformal Groups
• Quaternionic Quantization Principle in General Relativity and Supergravity
• Off-shell invariants of linearized $4D,\mathcal{N}=2$ supergravity in the harmonic approach
• Quaternion-Kähler N=4 Supersymmetric Mechanics
• Heterotic geometry without isometries
• Global Symmetries of Quaternion-K$\ddot{\mathbf{a}}$hler $\mathcal{N}=4$ Supersymmetric Mechanics