T-dualization of type II superstring theory in double space

Abstract In this article we offer a new interpretation of the T-dualization procedure of type II superstring theory in the double space framework. We use the ghost free action of type II superstring in pure spinor formulation in approximation of constant background fields up to the quadratic terms. T-dualization along any subset of the initial coordinates, $$x^a$$ x a , is equivalent to the permutation of this subset with subset of the corresponding T-dual coordinates, $$y_a$$ y a , in double space coordinate $$Z^M=(x^\mu ,y_\mu )$$ Z M = ( x μ , y μ ) . Requiring that the T-dual transformation law after the exchange $$x^a\leftrightarrow y_a$$ x a ↔ y a has the same form as the initial one, we obtain the T-dual NS–NS and NS–R background fields. The T-dual R–R field strength is determined up to one arbitrary constant under some assumptions. The compatibility between supersymmetry and T-duality produces a change of bar spinors and R–R field strength. If we dualize an odd number of dimensions $$x^a$$ x a , such a change flips type IIA/B to type II B/A. If we T-dualize the time-like direction, one imaginary unit i maps type II superstring theories to type $$\hbox {II}^\star $$ II ⋆ ones