Advantage of the second-order formalism in double space T-dualization of type II superstring

In this article we present bosonic T-dualization in double space of the type II superstring theory in the pure spinor formulation. We use the action with constant background fields obtained from the general case under some physically and mathematically justified assumptions. Unlike Nikolić and Sazdović (EPJ C 77:197, 2017), where we used the first-order theory, in this article fermionic momenta are integrated out. Full T-dualization in double space is represented as a permutation of the initial $$x^\mu $$xμ and T-dual coordinates $$y_\mu $$yμ. Requiring that a T-dual transformation law of the T-dual double coordinate $${}^\star Z^M=(y_\mu ,x^\mu )$$⋆ZM=(yμ,xμ) to be of the same form as for initial one $$Z^M=(x^\mu ,y_\mu )$$ZM=(xμ,yμ), we obtain the form of the T-dual background fields in terms of the initial ones. The advantage of using the action with integrated fermionic momenta is that it gives all T-dual background fields in terms of the initial ones. In the case of the first-order theory Nikolić and Sazdović (2017) a T-dual R-R field strength was obtained out of the double space formalism under additional assumptions.