Several observables in planar N=4 SYM, including the octagon anomalous dimension and Bremsstrahlung function, admit a once-subtracted dispersion representation over a positive measure in the coupling.
Null limit of large-charge correlators in planar $\mathcal{N}=4$ Super-Yang-Mills theory
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abstract
We present a conjecture for the double-logarithmic behavior of the logarithm of large-charge correlators in the null limit in planar $\mathcal{N} = 4$ Super-Yang-Mills theory. Generalizing earlier results for four- and five-point functions, our proposal predicts this behavior for $n$-point functions to all loops in terms of the tilted cusp anomalous dimension. In the dual amplitude description, it reproduces the expected small-mass behavior of massive amplitudes in the equal-mass limit.
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Positivity properties of observables in planar maximally supersymmetric Yang-Mills theory
Several observables in planar N=4 SYM, including the octagon anomalous dimension and Bremsstrahlung function, admit a once-subtracted dispersion representation over a positive measure in the coupling.