Wilson surfaces and higher dimensional knot invariants

Abstract

An observable for nonabelian, higher-dimensional forms is introduced, its properties are discussed and its expectation value in BF theory is described. This is shown to produce potential and genuine invariants of higher-dimensional knots.

31 pages, 9 figures

References in corpus (4)

• String Topology
• Higher-dimensional BF theories in the Batalin-Vilkovisky formalism: The BV action and generalized Wilson loops
• Topological Field Theory Interpretation of String Topology
• Loop observables for BF theories in any dimension and the cohomology of knots

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• On higher holonomy invariants in higher gauge theory I
• On higher holonomy invariants in higher gauge theory II
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• Configuration space integrals for embedding spaces and the Haefliger invariant
• On the global $2$-holonomy for a $2$-connection on a $2$-bundle
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• Formal Global AKSZ Gauge Observables and Generalized Wilson Surfaces
• Surface Operators in Superspace
• Wilson Surfaces for Surface Knots
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• Quantum field theoretic representation of Wilson surfaces: I higher coadjoint orbit theory
• Configuration space integral for long n-knots, the Alexander polynomial and knot space cohomology
• Quantum field theoretic representation of Wilson surfaces: II higher topological coadjoint orbit model
• BV Quantization
• Balloons and Hoops and their Universal Finite Type Invariant, BF Theory, and an Ultimate Alexander Invariant
• Cocycles of the space of long embeddings and BCR graphs with more than one loop
• On the space of injective linear maps from ${\mathbb{R}}^d$ into ${\mathbb{R}}^m$
• Topos Mediated Gravity: Toward the Categorical Resolution of the Cosmological Constant Problem