The OSp(32|1) versus OSp(8|2) supersymmetric M-brane action from self-dual (2,2) strings

Taking the (2,2) strings as a starting point, we discuss the equivalent integrable field theories and analyze their symmetry structure in 2+2 dimensions from the viewpoint of string/membrane unification. Requiring the Lorentz invariance and supersymmetry in the (2,2) string target space leads to an extension of the (2,2) string theory to a theory of 2+2 dimensional supermembranes (M-branes) propagating in a higher dimensional target space. The origin of the hidden target space dimensions of the M-brane is related to the maximally extended supersymmetry implied by the Lorentz covariance and dimensional reasons. The K"ahler-Chern-Simons-type action describing the self-dual gravity in 2+2 dimensions is proposed. Its maximal supersymmetric extension (of the Green-Schwarz-type) naturally leads to the 2+10 (or higher) dimensions for the M-brane target space. The proposed OSp(32|1) supersymmetric action gives the pre-geometrical description of M-branes, which may be useful for a fundamental formulation of F&M theory.Comment: 12 pages, LaTeX, misprints corrected, the final version to appear in the Modern Physics Letters

Exact hypermultiplet dynamics in four dimensions

We use N=2 harmonic and projective superspaces to formulate the most general `Ansatz' for the SU(2)_R invariant hypermultiplet low-energy effective action (LEEA) in four dimensions, which describes the two-parametric family of the hyper-K"ahler metrics generalizing the Atiyah-Hitchin metric. We then demonstrate in the very explicit and manifestly N=2 supersymmetric way that the (magnetically charged, massive) single hypermultiplet LEEA in the underlying non-abelian N=2 supersymmetric quantum field theory can receive both perturbative (e.g., in the Coulomb branch) and non-perturbative (e.g., in the Higgs branch) quantum corrections. The manifestly N=2 supersymmetric Feynman rules in harmonic superspace can be used to calculate the perturbative corrections described by the Taub-NUT metric. The non-perturbative corrections (due to instantons and anti-instantons) can be encoded in terms of an elliptic curve, which is very reminiscent to the Seiberg-Witten theory. Our four-dimensional results agree with the three-dimensional Seiberg-Witten theory and instanton calculations.Comment: 14 pages, LaTeX, 1 figure; substantial reduction (by 1/3