Note on graph-based BCJ relation for Berends-Giele currents

Abstract

Graph-based Bern-Carasso-Johansson (BCJ) relation for Berends-Giele currents in bi-adjoint scalar (BS) theory, which is characterized by connected tree graphs, was proposed in an earlier work. In this note, we provide a systematic study of this relation. We first prove the relations based on two special types of graphs: simple chains and star graphs. The general graph-based BCJ relation established by an arbitrary tree graph is further proved, through Berends-Giele recursion. When combined with proper off-shell extended numerators, this relation induces the graph-based BCJ relation for Berends-Giele currents in Yang-Mills theory. The corresponding relations for amplitudes are obtained via on-shell limits.

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.…”