Generalizations of the Double-Copy: the KLT Bootstrap

TL;DR

This work develops a bootstrap-based generalization of the KLT double-copy by treating the double-copy kernel as fixed by an identity element in a KLT algebra. By enforcing locality and KKBCJ-like constraints, the authors derive perturbative higher-derivative corrections to the BAS zeroth copy and its kernel, revealing a heterotic-type double-copy with distinct left and right sectors. They demonstrate concrete implementations in 4d Yang–Mills with higher-derivative corrections, producing dilaton–axion–gravity with local operators up to ∇^{10} R^4, and analyze 3-, 4-, and 5-point amplitudes, including SD/NSD sectors and comparisons to the string kernel. The paper also explores alternative zeroth-copy constructions, spurious-pole issues, and potential similarity-transform interpretations, laying groundwork for further exploration of generalized double-copies and their physical implications, including connections to Z-theory and positivity constraints.

Abstract

We formulate a new program to generalize the double-copy of tree amplitudes. The approach exploits the link between the identity element of the KLT algebra and the KLT kernel, and we demonstrate how this leads to a set of KLT bootstrap equations that the double-copy kernel has to satisfy (in addition to locality constraints). We solve the KLT bootstrap equations perturbatively to find the most general higher-derivative corrections to the 4- and 5-point field theory KLT kernel. The new kernel generalizes the string KLT kernel and its associated monodromy relations. It admits new color-structures in the effective theories it double-copies. It provides distinct generalized KK and BCJ relations for the left and right single-color theories and is in that sense a heterotic-type double-copy. We illustrate the generalized double-copy in detail for 4d Yang-Mills theory with higher-derivative corrections that produce dilaton-axion-gravity with local operators up order $\nabla^{10} R^4$. Finally, we initiate a search for new double-copy kernels.

Figures (1)

• Figure 1: Illustration of the physical meaning of the perturbative double-copy. Physics at the UV scale $\Lambda$ decouples in both the single- and double-copies as $\Lambda \rightarrow \infty$ (i.e. this diagram commutes) only if the rank of the higher-derivative corrected BAS is the same as the rank of the uncorrected BAS.