6,277 research outputs found
Hyper-complex four-manifolds from the Tzitz\'eica equation
It is shown how solutions to the Tzitz\'eica equation can be used to
construct a family of (pseudo) hyper-complex metrics in four dimensions.Comment: To be published in J.Math.Phy
Exact low-energy effective actions for hypermultiplets in four dimensions
We consider the general hypermultiplet Low-Energy Effective Action (LEEA)
that may appear in quantized, four-dimensional, N=2 supersymmetric, gauge
theories, e.g. in the Coulomb and Higgs branches. Our main purpose is a
description of the exact LEEA of n magnetically charged hypermultiplets. The
hypermultiplet LEEA is given by the N=2 supersymmetric Non-Linear Sigma-Model
(NLSM) with a 4n-dimensional hyper-K"ahler metric, subject to non-anomalous
symmetries. Harmonic Superspace (HSS) and the NLSM isometries are very useful
to constrain the hyper-K"ahler geometry of the LEEA. We use N=2 supersymmetric
projections of HSS superfields to N=2 linear (tensor) O(2) and O(4) multiplets
in N=2 Projective Superspace (PSS) to deduce the explicit form of the LEEA in
some particular cases. As the by-product, a simple new classification of all
multi-monopole moduli space metrics having su(2)_R symmetry is proposed in
terms of real quartic polynomials of 2n variables, modulo Sp(n)
transformations. The 4d hypermultiplet LEEA for n=2 can be encoded in terms of
an elliptic curve.Comment: 60 pages, LaTeX, macros included, references adde
Hyper-Kahler Sigma Models on (Co)tangent Bundles with SO(n) isometry
We construct N=2 supersymmetric nonlinear sigma models whose target spaces
are tangent as well as cotangent bundles over the quadric surface Q^{n-2} =
SO(n)/[SO(n-2)\times U(1)]. We use the projective superspace framework, which
is an off-shell formalism of N=2 supersymmetry.Comment: 33 pages, 1 figure, typos corrected, to appear in Nucl. Phys.
- …