Even-point multi-loop unitarity and its applications: exponentiation, anomalies and evanescence

We report on progress in understanding how to construct color-dual multi-loop amplitudes. First we identify a cubic theory, semi-abelian Yang-Mills, that unifies many of the color-dual theories studied in the literature, and provides a prescriptive approach for constructing D-dimensional color-dual numerators through one-loop directly from Feynman rules. By a simple weight counting argument, this approach does not further generalize to two-loops. As a first step in understanding the two-loop challenge, we use a D-dimensional color-dual bootstrap to successfully construct globally color-dual local two-loop four-point nonlinear sigma model (NLSM) numerators. The double-copy of these NLSM numerators with themselves, pure Yang-Mills, and $$\mathcal{N}$$ = 4 super-Yang-Mills correctly reproduce the known unitarity constructed integrands of special Galileons, Born-Infeld theory, and Dirac-Born-Infeld-Volkov-Akulov theory, respectively. Applying our bootstrap to two-loop four-point pure Yang-Mills, we exhaustively search the space of local numerators and find that it fails to satisfy global color-kinematics duality, completing a search previously initiated in the literature. We pinpoint the failure to the bowtie unitarity cut, and discuss a path forward towards non-local construction of color-dual integrands at generic loop order.

Revealing the landscape of globally color-dual multi-loop integrands

Edison,

Mangan,

Pavao

2024

No U(1) ‘electric-magnetic’ duality in Einstein gravity

Monteiro

2024

We revisit the question of whether classical general relativity obeys, beyond the linearised order, an analogue of the global U(1) electric-magnetic duality of Maxwell theory, with the Riemann tensor playing the role analogous to the field strength. Following contradictory claims in the literature, we present a simple gauge-invariant argument that the duality does not hold. The duality condition is the conservation of the helicity charge. Scattering amplitudes of gravitons in general relativity, and of gluons in Yang-Mills theory, violate this selection rule already at tree level. Indeed, the maximally-helicity-violating (MHV) amplitudes are famous for their simplicity. The duality in the linearised theories is, therefore, broken by the interactions. In contrast, the tree-level scattering amplitudes in duality-invariant theories of non-linear electromagnetism are known to obey helicity conservation. While the duality is not a symmetry of the full theory of general relativity, it does hold within a sector of the solution space, including vacuum type D solutions, where the duality is known to rotate between mass and NUT charge.

On the anomaly interpretation of amplitudes in self-dual Yang-Mills and gravity

Doran,

Monteiro,

Wikeley

2024

We investigate the integrability anomalies arising in the self-dual sectors of gravity and Yang-Mills theory, focusing on their connection to both the chiral anomaly and the trace anomaly. The anomalies in the self-dual sectors generate the one-loop all-plus amplitudes of gravitons and gluons, and have recently been studied via twistor constructions. On the one hand, we show how they can be interpreted as an anomaly of the chiral U(1) electric-magnetic-type duality in the self-dual sectors. We also note the similarity, for the usual fermionic chiral anomaly, between the 4D setting of self-dual Yang-Mills and the 2D setting of the Schwinger model. On the other hand, the anomalies in the self-dual theories also resemble the trace anomaly, sharing the same type of non-local effective action. We highlight the role of a Weyl-covariant fourth-order differential operator familiar from the trace anomaly literature, which (i) explains the conformal properties of the one-loop amplitudes, and (ii) indicates how this story may be extended to non-trivial spacetime backgrounds, e.g. with a cosmological constant. Moving beyond the self-dual sectors, and focusing on the gravity case, we comment on an intriguing connection to the two-loop ultraviolet divergence of pure gravity, whereby cancelling the anomaly at one-loop eliminates the two-loop divergence for the simplest helicity amplitudes.