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

TL;DR

This paper explores how T-duality transformations relate scattering amplitudes and Wilson loops in non-commutative super Yang-Mills theory by analyzing deformed AdS backgrounds and their dual geometries.

Contribution

It demonstrates the application of bosonic and fermionic T-duality to TsT-deformed AdS backgrounds and connects these transformations to gauge theory observables like scattering amplitudes and Wilson loops.

Findings

Dual geometry simplifies to AdS with a B-field depending on non-commutative parameters.

Scattering amplitudes and Wilson loops are computed in the deformed background.

Results establish a T-duality framework linking non-commutative gauge theories and string theory solutions.

Abstract

We first perform bosonic T-duality transformation on one of the marginal TsT (T-duality, shift, T-duality)-deformed $AdS_5\times S_5$ 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 $AdS_5\times S_5$ 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 $AdS_5\times S_5$ spacetime, which are dual to the null polygon Wilson loop and the folded string solution respectively in the final dual geometry.