A unified geometric framework for boundary charges and dressings: non-Abelian theory and matter
Boundaries in gauge theories are a delicate issue. We approach it through a geometric formalism based on the space of field configurations (field-space). Our main geometric tool is a connection 1-form on field-space, $\varpi$, which we introduce and explore in detail. Using it, we upgrade the presymplectic structure of Yang-Mills theory with boundaries to be invariant even under field-dependent gauge transformations. The gauge charges always vanish, while global charges still arise for configurations with global symmetries. The formalism is powerful because it is relational: the field-content itself is used as a reference frame to distinguish `gauge' and `physical'; no new degrees of freedom (e.g. group-valued edge modes) are required. Different choices of reference fields give different $\varpi$'s, which are related to gauge-fixings such as Higgs unitary and Coulomb gauge. But the formalism extends well beyond gauge-fixings, for instance by avoiding the Gribov problem. For one choice of $\varpi$, Goldstone modes arising from the condensation of matter degrees of freedom play precisely the role of known edge modes. For another choice, $\varpi$ is related to non-Abelian analogues of the Dirac dressing of the electron. Applied to the Lorentz symmetry of vielbein gravity, our formalism explains the origin of previously known Lorentz-invariant constructions. Lastly, we understand dressings as field-space Wilson lines for $\varpi$. We use the construction to unify the Lavelle-McMullan dressing with the gauge-invariant fields of Gribov-Zwanziger and Vilkovisky-DeWitt, and to put forward a notion of `historical dressing'.
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Henrique Gomes (add twitter)
Florian Hopfmüller (add twitter)
Aldo Riello (add twitter)
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08/07/18 05:54PM
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