Conformal Symmetry and Feynman Integrals

Simone Zoia

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arXiv · 1807.06020

Conformal Symmetry and Feynman Integrals

Simone Zoia

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Abstract

Singularities hidden in the collinear region around an external massless leg may lead to conformal symmetry breaking in otherwise conformally invariant finite loop momentum integrals. For an $\ell$-loop integral, this mechanism leads to a set of linear $2$nd-order differential equations with a non-homogeneous part. The latter, due to the contact nature of the anomaly in momentum space, is determined by $(\ell-1)$-loop information. Solving such differential equations in general is an open problem. In the case of 5-particle amplitudes up to two loops, the function space is known, and we can thus follow a bootstrap approach to write down the solution. As a first application of this method, we bootstrap the 6D penta-box integral.

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Simone Zoia. 2018-07-16. Conformal Symmetry and Feynman Integrals. https://arxiv.org/abs/1807.06020

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