2001/01/26 by Andrey Yu. Dubin, A. Yu. Dubin, Dubin, Andrey Yu.
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Conjecture #Coupling constant #FOS: Physical sciences #Gauge (firearms) #Gauge group #Gauge theory #Geometry #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Loop (graph theory) #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scaling #String (physics) #Wilson loop #Yang–Mills existence and mass gap #hep-lat #hep-ph #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0101182
57 pages
arxiv created 2001/01/26 · openalex publication_date 2001/01/26 · arxiv updated 2009/11/30 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
I adapt the Gauge String, representing the strong coupling (SC) expansion in the continuous D>=3 Yang-Mills theory (YMD) with a sufficiently large bare coupling constant λ>λcr and a fixed ultraviolet cut off Λ, to the analysis of the regularized Wilson's loop-averages. When generalized to describe the fat (rather than infinitely thin) flux-tubes, the pattern of thus modified U(N) Gauge String is proved to be consistent with the chain of the judiciously regularized U(N) Loop equations. In particular, we reveal the dimensional reduction YMD=>YM2, taking place in the extreme SC limit λ=>∞, and compare it with the implications of the AdS/CFT correspondence conjecture. On the other hand, for the loop-averages associated to the sufficiently large minimal areas, the proposed stringy pattern is supposed to be in the one infrared universality class (provided the loops are without zig-zag backtrackings) with the novel implementation of the noncritical D-dimensional Nambu-Goto string. The peculiarity is due to the nonstandard Λ2-scaling, Λ2=O(σph), of the physical string tension σph. Being well-motivated from the viewpoint of the standard YM4 theory with λ=>0, this scaling is argued to entail that the considered modification of the Nambu-Goto system is in the stringy (rather than in the branched polymer) regime. In sum, the confinement in the continuous D>=3 U(N) (and, similarly, SU(N)) gauge theory is justified, for the first time, at least when both N and λare sufficiently large. As a by-product, when continued to N=1, the Gauge String is shown to describe the continuous U(1) gauge theory with the monopoles.