The Partonic Nature of Instantons

TL;DR

This paper explores the partonic structure of instantons in lower-dimensional theories, providing explicit models and methods to identify their constituent degrees of freedom, with implications for understanding UV completions of higher-dimensional gauge theories.

Contribution

It offers a concrete, calculable model in 2+1 dimensions demonstrating instantons as multi-particle states with identifiable partons, advancing the partonic interpretation in non-renormalizable theories.

Findings

Single soliton in CP^N sigma-model is a multi-particle state.

Partons are identified with UV degrees of freedom.

Methods include model deformation and dual Bogomolnyi equations.

Abstract

In both Yang-Mills theories and sigma models, instantons are endowed with degrees of freedom associated to their scale size and orientation. It has long been conjectured that these degrees of freedom have a dual interpretation as the positions of partonic constituents of the instanton. These conjectures are usually framed in d=3+1 and d=1+1 dimensions respectively where the partons are supposed to be responsible for confinement and other strong coupling phenomena. We revisit this partonic interpretation of instantons in the context of d=4+1 and d=2+1 dimensions. Here the instantons are particle-like solitons and the theories are non-renormalizable. We present an explicit and calculable model in d=2+1 dimensions where the single soliton in the CP^N sigma-model can be shown to be a multi-particle state whose partons are identified with the ultra-violet degrees of freedom which render the theory well-defined at high energies. We introduce a number of methods which reveal the partons inside the soliton, including deforming the sigma model and a dual version of the Bogomolnyi equations. We conjecture that partons inside Yang-Mills instantons hold the key to understanding the ultra-violet completion of five-dimensional gauge theories.