New recursion relations for tree-level correlators in anti–de Sitter spacetime

Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents

“…Thus, to generalized the unifying relation (1) to curved spacetime, we introduce a semi-on-shell method which can escape from the on-shell subtlety in curved spacetime. The BG currents recursion stands out as its semi-onshell (semi-on-boundary in (A)dS) property [7,8,14]. In this subsection, we take the unifying relations between minimal coupled scalar and YM theory (5) as an example, and investigate the proof for (5) through the BG currents.…”

“…Similarly, substituting the scalar perturbiner expansion ansatz (14) into the equation of motion, we can obtain the BG currents for the scalars minimally couple to gluons:…”

“…We should emphasis that we do not impose the Lorenz gauge: k I • A I = 0. The interaction current [7,14] between gluons and minimal coupled scalars in (A)dS can be written as:…”

A type of unifying relation in (A)dS spacetime

“…As a semi-on-shell method, Berends-Giele (BG) currents [5] are popular because of their recursive character. In recent years, many techniques based on BG currents have been developed [6][7][8][9][10][11][12][13][14][15][16][17]. However, the research of BG currents in (A)dS is still very scarce.…”

“…However, in dS spacetime, only the factorization methods for 4-pt correlation functions are understood very well [28,29], thus it is still unknown whether they can be applied to this proof. Instead, BG currents recursion, as a semion-shell (semi-on-boundary) method, stands out because it is clearer than factorization methods in (A)dS [8]. In this paper, we discuss the "unifying relations" in (A)dS between…”