In late 2003, Edward Witten released a paper that revived the interest in Roger Penrose's twistors among particle physicists. The scattering amplitudes of gluons in $N=4$ gauge theory in four dimensions were expressed in a simple way using the twistor variables. Witten also proposed a particular model, the topological B-model on the $CP^{3|4}$ twistor space, to generate all these amplitudes.

These methods began their own life but the topological B-model became largely silent, perhaps partly because the phenomenologists who fell in love with these things haven't been trained in string theory, especially not in the topological one. However, many twistor-related discoveries in the recent 3 years - which were made without Witten's constructive picture - lead me to ask whether Witten's theory actually knows about these matters.

In particular, the "dual superconformal symmetry" was first noticed by Drummond et al. in 2006 and derived by stringy methods by Alday & Maldacena in 2008 or so. The 3+1 dimensions on the CFT boundary may be T-dualized to produce another copy of the Yang-Mills theory that is superconformally invariant once again. Scattering amplitudes have been converted to the expectation values of piecewise linear Wilson loops in the dual theory - the segments have the directions and length of the light-like momenta of the scattering particles. My question is

**Can you also "T-dualize" Witten's topological B-model to obtain another one in which the scattering amplitudes are computed in a different way?**

If you think that the answer is Yes, I would also like to know what is the "dual prescription" for the supersymmetric Yang-Mills amplitudes and whether the D1- and D5-branes in Witten's original models are replaced by other D1- and D5-branes or, for example, by D3-branes.

This post imported from StackExchange Physics at 2014-06-07 05:12 (UCT), posted by SE-user Luboš Motl