The Partonic Nature of Instantons

Details The Partonic Nature of Instantons The Partonic Nature of Instantons

2009-05-14

arxiv.org/abs/0905.2267v2

JHEP 0908:006,2009

Physics

High Energy Physics

High Energy Physics - Theory

28 pages. v3: extra references and comments. Mathematica notebooks for the figures can be downloaded from http://www.damtp.c

Scientific paper

10.1088/1126-6708/2009/08/006

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.

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