T-duality to Scattering Amplitude and Wilson Loop in Non-commutative Super Yang-Mills Theory

Abstract

We first perform bosonic T-duality transformation on one of the marginal TsT (T-duality, shift, T-duality)-deformed $Ad{S}_5\times S_5$ spacetime, which corresponds to 4D $\mathcal{N}=4$ 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 $Ad{S}_5\times S_5$ but with the 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 $Ad{S}_5\times S_5$ spacetime, which are dual to the null polygon Wilson loop and the folded string solution respectively in the final dual geometry.

24 pages, latex, references added, published version

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