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 ∇10R4. Finally, we initiate a search for new double-copy kernels.
Highlights
Beginning with the pioneering discovery of Kawai-Lewellen-Tye (KLT) [1], the existence of a multiplicative structure, called the double-copy, on the space of relativistic field theories and string theories has become an indispensable tool for the study of scattering amplitudes and beyond
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
In much of the Introduction we have focused on generalizations of the double-copy that arise from adding higher-derivative operators to the bi-adjoint scalar theory (BAS) model, but one can look for other types of solutions to the KLT bootstrap equations
Summary
Beginning with the pioneering discovery of Kawai-Lewellen-Tye (KLT) [1], the existence of a multiplicative structure, called the double-copy, on the space of relativistic field theories and string theories has become an indispensable tool for the study of scattering amplitudes and beyond. In which the multiplication rule ⊗ is determined by the double-copy kernel Sn. A key feature is that both the field theory and string theory KLT double-copy maps contain an identity element: a model whose tree amplitudes double-copy with the L/R tree amplitudes of single-copy models to give those same L/R amplitudes as output. Can, in the small α -expansion, be viewed as the BAS model with a very particular selection of higher-derivative corrections, all with coefficients completely fixed in terms of α This motivates the study of the class of double-copy kernels that arise from the most general deformations of the BAS zeroth copy model with local higher-derivative (h.d.). The Introduction ends with an overview of results and an outline of the rest of the paper
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