N=2 supersymmetric sigma-models and duality

作者：Kuzenko Sergei M^*

来源：The Journal of High Energy Physics, 2010, (1): 115.

DOI：10.1007/JHEP01(2010)115

• Supersymmetry and Duality
• Extended Supersymmetry
• Superspaces
• Supersymmetric Effective Theories

For two families of four-dimensional off-shell N = 2 supersymmetric nonlinear sigma-models constructed originally in projective superspace, we develop their formulation in terms of N = 1 chiral superfields. Specifically, these theories are:
(i) sigma-models on cotangent bundles T*M of arbitrary real analytic Kahler manifolds M;
(ii) general superconformal sigma-models described by weight-one polar supermultiplets.
Using superspace techniques, we obtain a universal expression for the holomorphic symplectic two-form omega((2,0)) which determines the second supersymmetry transformation and is associated with the two complex structures of the hyperkahler space T*M that are complimentary to the one induced from M. This two-form is shown to coincide with the canonical holomorphic symplectic structure. In the case (ii), we demonstrate that omega((2,0)) and the homothetic conformal Killing vector determine the explicit form of the superconformal transformations. At the heart of our construction is the duality (generalized Legendre transform) between off-shell N = 2 supersymmetric nonlinear sigma-models and their on-shell N = 1 chiral realizations. We finally present the most general N = 2 superconformal nonlinear sigma-model formulated in terms of N = 1 chiral superfields. The approach developed can naturally be generalized in order to describe 5D and 6D superconformal nonlinear sigma-models in 4D N = 1 superspace.

• 出版日期2010-1