Three Proofs of the Makeenko–Migdal Equation for Yang–Mills Theory on the Plane

We give three short proofs of the Makeenko–Migdal equation for the Yang–Mills measure on the plane, two using the edge variables and one using the loop or lasso variables. Our proofs are significantly simpler than the earlier pioneering rigorous proofs given by Lévy and by Dahlqvist. In particular,...

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Bibliographic Details
Published in:Communications in mathematical physics 2017-04, Vol.351 (2), p.741-774
Main Authors: Driver, Bruce K., Hall, Brian C., Kemp, Todd
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Mills
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Yang-Mills theory
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Summary:We give three short proofs of the Makeenko–Migdal equation for the Yang–Mills measure on the plane, two using the edge variables and one using the loop or lasso variables. Our proofs are significantly simpler than the earlier pioneering rigorous proofs given by Lévy and by Dahlqvist. In particular, our proofs are “local” in nature, in that they involve only derivatives with respect to variables adjacent to the crossing in question. In an accompanying paper with Gabriel, we show that two of our proofs can be adapted to the case of Yang–Mills theory on any compact surface.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-016-2793-6