Event

Aldo Riello, Perimeter Institute

Tuesday, November 20, 2018 15:30to16:30
Room 4336, Pav. André-Aisenstadt, 2920, ch. de la Tour, CA

A unified geometric framework for Yang-Mills charges and dressings in finite regions

Boundaries and finite regions in gauge theories are a delicate issue. I approach it through a geometric formalism based on the space of field configurations (field-space). The main geometric tool is a connection 1-form on field-space, ϖ. In the first part of the talk, I introduce ϖ and explore its properties, especially vis-à-vis gauge fixings and boundary conditions. Then I use it to upgrade the Yang-Mills (pre)symplectic structure in presence of boundaries to make it invariant even under field-dependent gauge transformations. A comparison to “edge modes” is quickly presented. In the second part of the talk, I introduce an explicit and natural example of ϖ constructed solely out of the gauge-potential (Singer-DeWitt). In particular, I show that: (i) the corresponding ϖ-upgraded symplectic form naturally selects global gauge charges at reducible configurations (e.g. the total electric charge), while projecting out all other “pure-gauge” charges; and that (ii) the field-space holonomies of the Singer-DeWitt ϖ are natural dressing factors (e.g. Dirac’s dressing in electrodynamics) which implicitly underlaid the construction of the Vilkovisky-DeWitt geometric action. Time allowing, I will also consider a ϖ constructed only out of matter fields (Higgs) and discuss the corresponding dressings and relations to spontaneously broken gauge symmetries. This talk is based on work done in collaboration with H. Gomes (and F. Hopfmueller). Refs: 1808.02074 features a complete account, while 1804.01919 briefly presents the basic ideas exemplified in the simple Abelian context. The first paper of the series, 1608.08226 , sketches some ideas about gravity and other applications, but is less complete under other respects.

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