1996/07/03 by M. Alvarez, Mercedes Álvarez, J.M.F. Labastida +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structure #Black Holes and Theoretical Physics #Chern–Simons theory #Factorization #Gauge group #Gauge theory #Geometric and Algebraic Topology #Mathematical physics #Mathematics #Pure mathematics #Wilson loop #hep-th #math.QA #q-alg
paper · pdf · doi:10.1016/s0550-3213(96)00689-x
published as Nucl.Phys. B488 (1997) 677-718 · 44 pages, LaTex, epsf.sty, 15 figures
arxiv created 1996/07/03 · openalex publication_date 1997/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The general structure of the perturbative expansion of the vacuum expectation value of a product of Wilson-loop operators is analyzed in the context of Chern-Simons gauge theory. Wilson loops are opened into Wilson lines in order to unravel the algebraic structure encoded in the group factors of the perturbative series expansion. In the process a factorization theorem is proved for Wilson lines. Wilson lines are then closed back into Wilson loops and new link invariants of finite type are defined. Integral expressions for these invariants are presented for the first three primitive ones of lower degree in the case of two-component links. In addition, explicit numerical results are obtained for all two-component links of no more than six crossings up to degree four.