D = 2, Script N = (2, 2) semi chiral vector multiplet

We describe a new 1 + 1 dimensional = (2, 2) vector multiplet that naturally couples to semi chiral superfields in the sense that the gauged supercovariant derivative algebra is only consistent with imposing covariantly semi chiral superfield constraints. It has the advantage that its prepotentials shift by semi chiral superfields under gauge transformations. We also see that the multiplet relates the chiral vector multiplet with the twisted chiral vector multiplet by reducing to either multiplet under appropriate limits without being reducible in terms of the chiral and twisted chiral vector multiplet. This is explained from the superspace geometrical point of view as the result of possessing a symmetry under the discrete supercoordinate transformation that is responsible for mirror copies of supermultiplets. We then describe how to gauge a non linear sigma model with semi chiral superfields using the prepotentials of the new multiplet.