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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.04222 |
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Table of Contents:
- The leading order $N$-point energy correlators of maximally supersymmetric Yang-Mills theory in the limit where the $N$ detectors are collinear can be expressed as an integral of the $1\to N$ splitting function, which is given by the $(N{+}3)$-point squared super-amplitudes at tree level. This provides yet another example that the integrand of certain physical observable -- $N$-point energy correlator -- is computed by the canonical form of a positive geometry -- the (tree-level) "squared amplituhedron". By extracting such squared amplitudes from the $f$-graph construction, we compute the integrand of energy correlators up to $N=11$ and reveal new structures to all $N$; we also show important properties of the integrand such as soft and multi-collinear limits. Finally, we take a first look at integrations by studying possible residues of the integrand: our analysis shows that while this gives prefactors in front of multiple polylogarithm functions of $N=3,4$, the first unknown case of $N=5$ already involves elliptic polylogarithmic functions with many distinct elliptic curves, and more complicated curves and higher-dimensional varieties appear for $N>5$.