The Sheffield Theaters’ revival of “Democracy,” the cold-war spy drama by Michael Frayn (“Noises Off”), will transfer to London’s Old Vic Theater for a limited four week run starting June 15.Frayn’s play premiered at the National Theater in 2003, won the Evening Standard Award and Critics’ Circle Awards for best play and transferred for a five-month West End run in 2004. “Democracy” also landed on Broadway in 2004. The current production, helmed by Sheffield Crucible associate director Paul Miller, ran as part of a season of plays there in advance of the playwright’s 80th birthday in 2013. The Old Vic’s recent revival of Frayn’s farce “Noises Off” has transferred to the West End’s Novello Theater. The current Old Vic production, Jamie Lloyd’s hit revival of “The Duchess of Malfi” starring Eve Best, completes its run on June 9.