Harmonic Superspace from the $AdS_5\times S^5$ Pure Spinor Formalism
  On-shell supergravity vertex operators in an $AdS_5\times S^5$ background are described in the pure spinor formalism by the zero mode cohomology of a BRST operator. After expanding the pure spinor BRST operator in terms of the $AdS_5$ radius variable, this cohomology is computed using N=4 harmonic superspace variables and explicit superfield expressions are obtained for the behavior of supergravity vertex operators near the boundary of $AdS_5$. 
Nathan Berkovits and Thiago Fleury (ICTP-SAIFR/IFT-UNESP, Sao Paulo)
hep-th