Alternative N = (4, 0) superstring and σ-models

We present an alternative N = (4, 0) superstring theory, with a field content different from that of previously-known N = (4, 0) superstring theories. This theory is presented as a non-linear σ-model on the coset SU(n,1)SU(n) ⊗ U(1) as the target space-time with torsion, which is coupled to N = (4,0) world-sheet superconformal gravity. Our result indicates that the target space-time for the N = 4 superstring theory does not necessarily have to be a hyper-Kähler or quaternionic Kähler manifold.