Supersymmetric Nonlinear Sigma Models on Ricci-flat Kähler Manifolds with O(N) Symmetry

We propose a class of N = 2 supersymmetric nonlinear sigma models on the Ricci-flat Kähler manifolds with O(N) symmetry. ∗ E-mail: [email protected] † E-mail: [email protected] ‡ E-mail: [email protected] String theory propagating in a curved spacetime is described by a conformal invariant nonlinear sigma model in two dimensions. Spacetime supersymmetry of the string theory requires N = 2 worldsheet supersymmetry. The conformal invariance is realized in finite field theories with vanishing β functions. In this letter, we propose a class of nonlinear sigma models on Ricci-flat Kähler manifolds with O(N) symmetry. Two-dimensional N = 2 supersymmetric nonlinear sigma models are described by (anti-)chiral superfields: φ = A + √ 2θψ + θθF (φ = A + √ 2 θψ + θθF ) where A, ψ and F are complex scalar, Dirac fermion, auxiliary scalar fields, respectively. To define supersymmetric nonlinear sigma models on the Ricci-flat Kähler manifolds with O(N) symmetry, we prepare dynamical chiral superfields φi (i = 1, · · · , N ; N ≥ 2), belonging to the vector representation of O(N), and an auxiliary chiral superfield φ0, belonging to an O(N) singlet. The most general Lagrangian with O(N) symmetry, composed of these chiral superfields, is given by L = ∫