Double Soft Theorems in Gauge and String Theories

TL;DR

The paper establishes universal multi-soft theorems in gauge and open-string theories at tree level, showing that double-soft gluon limits with opposite helicities contain nontrivial corrections beyond product of single-soft factors, while double-soft gravitons factorize simply as products of single-soft contributions. It derives these results through both BCFW recursion in four dimensions and CHY formulas in arbitrary dimensions, and extends the analysis to triple-soft gluons and multi-soft gravitons. In supersymmetric theories, the authors uncover soft scalar and fermion theorems governed by R-symmetry generators acting on lower-point amplitudes, with precise formulations in N=4 and pure N=2 SYM, including SUSY-reduced cases. Strikingly, the double-soft-scalar theorems persist to open superstring theory without alpha' corrections, highlighting a robust universality of these soft behaviors across gauge and string theories.

Abstract

We investigate the tree-level S-matrix in gauge theories and open superstring theory with several soft particles. We show that scattering amplitudes with two or three soft gluons of non-identical helicities behave universally in the limit, with multi-soft factors which are not the product of individual soft gluon factors. The results are obtained from the BCFW recursion relations in four dimensions, and further extended to arbitrary dimensions using the CHY formula. We also find new soft theorems for double soft limits of scalars and fermions in N=4 and pure N=2 SYM. Finally, we show that the double-soft-scalar theorems can be extended to open superstring theory without receiving any alpha' corrections.