Mellin amplitude for $n$-gluon scattering in anti–de Sitter spacetime

In AdS/CFT, we introduce a robust method for computing $n$-point gluon Mellin amplitudes, applicable in various spacetime dimensions. Using the Mellin transform and a recursive algorithm, we efficiently calculate tree-level gluon amplitudes. Our approach simplifies the representation of higher-point amplitudes, eliminating the need for complicated integrations. Crucially, the resulting amplitudes closely mirror those in flat space, allowing a straightforward dictionary between the two settings circumventing explicit calculations.

Figure 1

Schematic of how $n+1$ Mellin amplitude factorizes into two subamplitudes.

Figure 2

(a)–(i) From simple to complex: A compendium of tree-level higher-point Witten diagrams for gluons.

Figure 3

Decoding the complexity: topology of eight-point “drone diagrams” as a representative example (4.2).