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The Three-Point Form Factor of $\textrm{Tr}\,\phi^3$ to Six Loops

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arxiv 2410.22402 v1 pith:DIYECJGX submitted 2024-10-29 hep-th hep-ph

Benjamin Basso , Lance J. Dixon , Alexander G. Tumanov This is my paper · ORCID
classification hep-thhep-ph
keywords factorformlimitoperatortextrmdescribingffopefind
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

We study the three-point form factor of the length-three half-BPS operator ($\textrm{Tr}\,\phi^3$) in planar $\mathcal{N}=4$ Super-Yang-Mills theory, using analyticity and integrability methods. We find that the functions describing the form factor in perturbation theory live in the same restrictive space of multiple polylogarithms as the one describing the form factor of the stress-tensor operator ($\textrm{Tr}\,\phi^2$). Furthermore, we find that the leading-order data in the collinear limit provided by the form factor operator product expansion (FFOPE) is enough to fix the form factor uniquely, at least through six loops. We perform various tests of our results using the subleading FFOPE corrections. We also analyze the form factor in the Regge limit where two Mandelstam invariants are large; we obtain a compact representation for the form factor in this limit which is valid to all orders in the coupling.

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Cited by 7 Pith papers

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