T-duality to scattering amplitude and Wilson loop in non-commutative super Yang-Mills theory

Abstract

Abstract We first perform bosonic T-duality transformation on one of the marginal TsT (T-duality, shift, T-duality)-deformed AdS 5×S 5 spacetime, which corresponds to 4D $$ \mathcal{N}=4 $$ N = 4 non-commutative super Yang-Mills theory (NCSYM). We then construct the solution to Killing spinor equations of the resulting background, and perform the fermionic T-duality transformation. The final dual geometry becomes the usual AdS 5 × S 5 spacetime but with a constant NS-NS B-field depending on the non-commutative parameter. As applications, we study the gluon scattering amplitude and open string (Wilson loop) solution in the TsT-deformed AdS 5 × S 5 spacetime, which are dual to the null polygon Wilson loop and the folded string solution respectively in the final dual geometry.