  The twistor superstring, which describes N=4 super Yang-Mills trees, is taken
off-shell (for loops) by generalizing Penrose twistors (which describe on-shell
momenta) to Atiyah-Drinfel'd-Hitchin-Manin twistors (which include the usual
spacetime coordinates). The resulting string is then shown to be the
tensionless limit of a Quantum ChromoDynamics-like superstring.
