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 AdS 5 × S 5 spacetime, which corresponds to 4D N = 4 noncommutative 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 TsTdeformed 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.

Geometries with twisted spheres and non-abelian T-dualities

“…Over the last three decades, studies of dualities in string theory have led to many remarkable results, ranging from discovery of D-branes [1][2][3][4][5] and M-theory [6][7][8] to insights into physics JHEP03(2024)102 of black holes [9][10][11][12] and AdS/CFT correspondence [13][14][15][16]. In particular, combinations of T-dualities and coordinate transformations have played an important role in understanding of charged black holes [17][18][19][20][21] and gravity duals of various field theories [22][23][24][25][26][27][28][29][30][31][32][33]. These combinations, known as TsT transformations [28,34,35], involve stringy backgrounds with abelian isometries, and they rely on Buscher rules for the duality maps [36].…”