Abstract
A
bstract
We propose a bootstrap program for the
form factor squared
with operator tr(
ϕ
2
) in maximally supersymmetric Yang-Mills theory in the planar limit, which plays a central role for perturbative calculations of important physical observables such as energy correlators. The tree-level
N
-point form factor (FF) squared can be obtained by cutting
N
propagators of a collection of two-point “master diagrams” at (
N
– 1) loops: for
N
= 3, 4, 5, 6 there are merely 1, 2, 4, 13 topologies of such diagrams respectively, and their numerators are strongly constrained by power-counting (including “no triangle” property) and other constraints such as the “rung rule”. Moreover, these two-point diagrams provide a “unification” of FF squared at different numbers of loops and legs, which is similar to extracting (planar) amplitude squared from vacuum master diagrams (dual to
f
-graphs): by cutting 2 ≤
n
N
propagators, one can also extract the planar integrand of
n
-point FF squared at (
N
–
n
) loops, thus our results automatically include integrands of 2-point (Sudakov) FF up to four loops (where the squaring is trivial), 3-point FF squared up to three loops, and so on. Our ansatz is completely fixed using soft limits of (tree and loop) FF squared and the multi-collinear limit which reduces it to the splitting function, without any other inputs such as unitarity cuts. This method opens up the exciting possibility of a
graphical bootstrap
for FF squared for higher
N
(which contains e.g. planar Sudakov FF to
N
– 2 loops) similar to that for the amplitude squared via
f
-graphs. We also comment on applications to the computation of leading order energy correlators where new structures are expected after performing phase-space integrations.