A reparametrization invariant surface ordering

Abstract

We introduce a notion of a non-Abelian loop gauge field defined on points in loop space. For this purpose we first find an infinite-dimensional tensor product representation of the Lie algebra which is particularly suited for fields on loop space. We define the non-Abelian Wilson surface as a `time' ordered exponential in terms of this loop gauge field and show that it is reparametrization invariant.

11 pages, clarifications and added refs

References in corpus (3)

• Nonabelian 2-forms and loop space connections from SCFT deformations
• Gerbes, covariant derivatives, p-form lattice gauge theory, and the Yang-Baxter equation
• Towards the Theory of Non--Abelian Tensor Fields II

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• The non-Abelian tensor multiplet in loop space
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• Non-Geometric Magnetic Flux and Crossed Modules
• Closed non-abelian strings
• In quest of a generalized Callias index theorem