Becchi-Rouet-Stora-Tyutin-Lagrangian Double Copy of Yang-Mills Theory

Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

“…1 The chief advantages of the convolution, including the extra BRST fields, are that (i) the ghost sector allows the dilaton to be truncated without imposing further constraints on the graviton [6,71] and (ii) the Yang-Mills gauge choice determines the N = 0 supergravity gauge choice to linear order, removing the ambiguities inherent in, for example, the double-copy of gauge dependent solutions. In [72,73] it was shown that tree-level CK duality holds for amplitudes involving all states of the BRST Fock space, including the unphysical longitudinal gluon and ghost modes, and that this can be made manifest in a purely cubic Yang-Mills BRST-Lagrangian. 2 It was then shown that its Lagrangian double-copy yields a BRST-Lagrangian that is pertubatively quantum equivalent to N = 0 supergravity to all orders, tree and loop [72,73].…”

“…In [72,73] it was shown that tree-level CK duality holds for amplitudes involving all states of the BRST Fock space, including the unphysical longitudinal gluon and ghost modes, and that this can be made manifest in a purely cubic Yang-Mills BRST-Lagrangian. 2 It was then shown that its Lagrangian double-copy yields a BRST-Lagrangian that is pertubatively quantum equivalent to N = 0 supergravity to all orders, tree and loop [72,73]. A direct corollary is that all tree and loop Yang-Mills amplitude integrands can be written in a form that double-copies correctly, i.e.…”

“…Of course, for free gauge and gravity theories, the ghosts decouple and there is no need to pass through BRST. However, it is nonetheless important in the context of squaring Yang-Mills theory [2,4,6,72,73].…”

“…Both of these hurdles, however, seem surmountable. One other important extension would be to construct the gravitational theories to higher orders perturbatively on these backgrounds, as was done for flat backgrounds in [6,72,73,86]. Here one could exploit recent developments extending color-kinematics duality to these spaces [80,81].…”

“…Although tree-level CK duality holds for all states of the extended BRST Fock space, this does not necessarily imply loop-level CK duality. However, the gluon loop amplitude integrands computed with the Feynman diagrams of the manifest BRST-CK dual Yang-Mills action of[72,73] provide 'almost BCJ numerators' that double-copy correctly into the loop amplitude integrands of N = 0 supergravity[72,73].…”