T T ¯ deformation of N= (1,1) off-shell supersymmetry and partially broken supersymmetry

We construct the superaction for the TT¯ deformation of 2D free N=(1,1) supersymmetric model with a deformed superfield. We show that the N=(1,1) off-shell supersymmetry in the free theory is deformed under the TT¯ deformation, which is incorporated in the deformed superfield. We interpret this superaction as an effective action of the Goldstone superfield for the partial spontaneous breaking of N=(2,2) supersymmetry to N=(1,1). We show that the unbroken and broken supersymmetry of the effective superaction corresponds to the off-shell N=(1,1) supersymmetry and the off-shell Fermi global nonlinear symmetry in the TT¯-deformed theory, respectively. We demonstrate that this effective superaction can be obtained by the nonlinear realization of the partially broken global supersymmetry (PBGS) from the coset superspace. Furthermore, we reproduce the superaction by the constrained superfield method accompanied by a field redefinition.