Linear relations between N >= 4 supergravity and subleading-color SYM amplitudes
Stephen G. Naculich, Horatiu Nastase, Howard J. Schnitzer
TL;DR
The paper extends the BCJ color-kinematic duality and gravity–gauge theory double-copy framework to derive linear relations between $ abla N+4$ supergravity amplitudes and the most-subleading-color SYM amplitudes for $L=1,2$ at four points and $L=1$ at five points, covering $ abla N=4,5,6$ supergravity and $ abla N=0,1,2$ SYM. It presents explicit formulas linking gravity amplitudes to the SYM-subleading-color data, including a unified expression for the four-point case and a pentagon-based five-point relation, all grounded in BCJ-dual numerators that can be used in double copies. The IR-divergence analysis shows that the leading $1/ abla$ (and higher) poles of subleading-color amplitudes align with the $L$-loop gravity divergences, supporting the interpretation of these amplitudes as a basis for gravity expansions. The work also demonstrates consistency conditions for IR structures, deriving BCJ-type constraints on kinematic coefficients and highlighting the broad applicability to $N eq 4$ SYM and even to pure Yang–Mills, with potential implications for QCD-like theories.
Abstract
The IR divergences of supergravity amplitudes are less severe than those of planar SYM amplitudes, and are comparable to those subleading-color SYM amplitudes that are most subleading in the 1/N expansion, namely O(1/epsilon^L) for L-loop amplitudes. We derive linear relations between one- and two-loop four-point amplitudes and one-loop five-point amplitudes of N = 4, 5, and 6 supergravity and the most-subleading-color contributions of the analogous amplitudes of N = 0, 1, and 2 SYM theory, extending earlier results for N = 8 supergravity amplitudes. Our work relies on linear relations between N >= 4 supergravity and planar SYM amplitudes that were recently derived using the double-copy property of gravity, and color-kinematic duality of gauge theories.