Bootstrap Methods for the Soft Anomalous Dimension

Quantum field theory-the mathematical framework that allows physicists to probe the basic microscopic laws of the universe-has given rise to some of the most precise predictions in the history of science. Even so, methods for carrying out calculations in quantum field theory remain tragically underdeveloped, to the extent that the results of arduous multi-year calculations are regularly observed to collapse to unexpectedly-simple expressions only in the last step.

This indicates that a dramatic change is required in how we go about carrying out these computations in order to properly account for this mathematical simplicity.

Over the last few years, novel bootstrap methods have been developed that leverage our increasingly refined understanding of the mathematical structure of scattering amplitudes in order to construct their functional form directly. These new methods have already given rise to some of the highest-order results in perturbative quantum field theory, extending in some cases up to eight loops.

The goal of this project will be to extend these bootstrap methods to one of the key quantities that appears in the Standard Model of particle physics: the soft anomalous dimension, which describes the universal infrared structure of gauge theory amplitudes. This object is of both theoretical and phenomenological interest, as it is essential for making predictions for particle collider experiments. More concretely, the goals of this project will be to:

- derive new constraints on the discontinuities that can appear in the soft anomalous dimension, from basic physical principles such as causality and locality - construct the space of functions that the soft anomalous dimension is expected to evaluate to at three and four loops - calculate the soft anomalous dimension as an expansion around special kinematic limits

Together, these results should allow us to bootstrap the soft anomalous dimension directly from mathematical and physical constraints, thereby sidestepping the difficult integration problems that currently hinder its evaluation."