Abstract
We generalize the unifying relations for tree amplitudes to the 1-loop Feynman integrands. By employing the 1-loop CHY formula, we construct differential operators which transmute the 1-loop gravitational Feynman integrand to Feynman integrands for a wide range of theories, including Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory, bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon theory. The unified web at 1-loop level is established. Under the well known unitarity cut, the 1-loop level operators will factorize into two tree level operators. Such factorization is also discussed.
Highlights
For reader’s convenience, we rapidly review the necessary background
In the CHY framework, tree amplitudes for n massless particles in arbitrary dimensions arise from a multi-dimensional contour integral over the moduli space of genus zero Riemann surfaces with n punctures, M0,n [5,6,7,8,9], formulated as
By applying the operator T◦C[+, σ1, · · ·, σn, −] defined as summing over T◦ [+, σ1, · · ·, σn, −] cyclicly, the bi-adjoint scalar (BAS) Feynman integrand can be generated from the YM Feynman integrand, and the YM Feynman integrand can be generated from the GR Feynman integrand, as can be seen in subsection 3.4
Summary
For reader’s convenience, we rapidly review the necessary background. In subsection 2.1, we give a brief introduction to the CHY formula at the tree level. In subsection 2.2, we review the forward limit method, as well as the CHY formula at the 1-loop level. The tree level differential operators, which link the tree level amplitudes of a wide range of theories together, will be introduced in subsection 2.3
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
