Differential operators built from the 1-loop CHY formula map the gravitational 1-loop Feynman integrand to those of Einstein-Yang-Mills, pure Yang-Mills, Born-Infeld, bi-adjoint scalar, and other theories, with factorization into tree-level operators under unitarity cuts.
Loop Integrands for Scattering Amplitudes from the Riemann Sphere
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abstract
The scattering equations on the Riemann sphere give rise to remarkable formulae for tree-level gauge theory and gravity amplitudes. Adamo, Casali and Skinner conjectured a one-loop formula for supergravity amplitudes based on scattering equations on a torus. We use a residue theorem to transform this into a formula on the Riemann sphere. What emerges is a framework for loop integrands on the Riemann sphere that promises to have wide application, based on off-shell scattering equations that depend on the loop momentum. We present new formulae, checked explicitly at low points, for supergravity and super-Yang-Mills amplitudes and for n-gon integrands at one loop. Finally, we show that the off-shell scattering equations naturally extend to arbitrary loop order, and we give a proposal for the all-loop integrands for supergravity and planar super-Yang-Mills theory.
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Develops worldsheet sigma model for fundamental strings in critical type IIA limit showing nodal singularities and derives T-duality web unifying decoupling limits including ambitwistor and Carrollian strings.
New differential operators transmute 1-loop gravitational integrands to Yang-Mills ones and enable a unified web of expansions relating integrands of gravity, gauge, scalar and effective theories.
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On differential operators and unifying relations for $1$-loop Feynman integrands
Differential operators built from the 1-loop CHY formula map the gravitational 1-loop Feynman integrand to those of Einstein-Yang-Mills, pure Yang-Mills, Born-Infeld, bi-adjoint scalar, and other theories, with factorization into tree-level operators under unitarity cuts.
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Worldsheet Formalism for Decoupling Limits in String Theory
Develops worldsheet sigma model for fundamental strings in critical type IIA limit showing nodal singularities and derives T-duality web unifying decoupling limits including ambitwistor and Carrollian strings.
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Transmutation operators and expansions for $1$-loop Feynman integrands
New differential operators transmute 1-loop gravitational integrands to Yang-Mills ones and enable a unified web of expansions relating integrands of gravity, gauge, scalar and effective theories.