Supersymmetric twists in twistor space and holography

A bstract We compute some supersymmetric twists of field theories in twistor space, including the minimal supersymmetric and the chiral algebra twists of supersymmetric self-dual Yang-Mills, and the minimal twist of N N = 1 self-dual supergravity. In the case of N N = 4 we also find their holographic duals in the framework of chiral holography. We find that the minimal twist of gauge theories in twistor space is a topological-holomorphic theory and show that they are perturbatively and BRST equivalent to known holomorphic theories on spacetime at the classical level. We show that this is a consequence of the holomorphic degrees of freedom being effectively localized to a point on the twistor sphere making the choice of complex structure on spacetime manifest. For superconformal theories, the twist further localizes the holomorphic degrees of freedom to a plane contained on spacetime, reproducing the chiral algebra twist of N N = 4 sYM. We show that the bulk duals of these twists also give lower dimensional holomorphic theories, reproducing results from twisted holography.