Confinement for all values of the coupling in four-dimensional SU(2) gauge theory

Abstract

A derivation is given from first principles of the fact that the SU(2) gauge theory is in a confining phase for all values of the coupling $0<g<\infty$ defined at lattice spacing (UV regulator) $a$, and space-time dimension $d\le 4$. The strategy is to employ approximate RG decimation transformations of the potential moving type which give both upper and lower bounds on the partition function at each successive decimation step. By interpolation between these bounds an exact representation of the partition function is obtained on progressively coarser lattices. In the same manner, one obtains a representation of the partition function in the presence of external center flux. Under successive decimations the flow of the effective action in these representations is constrained by that in the upper and lower bounds which are easily explicitly computable. Confining behavior for the vortex free energy order parameter (ratio of partition functions with and without external flux), hence `area law' for the Wilson loop, is the result for any initial coupling. Keeping the string tension fixed determines the dependence $g(a)$, which is such that $g(a)\to 0$ for $a\to 0$.

49 pages, 3 figures

Cited by in corpus (7)

• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Entanglement entropy in d+1 SU(N) gauge theory
• Reply to arXiv:0711.4930[hep-th] by Ito and Seiler
• A theorem concerning twisted and untwisted partition functions in U(N) and SU(N) lattice gauge theories
• Exploring the QCD vacuum - (some) recent developments in confinement and topology
• Vortex topology and the continuum limit of lattice gauge theories
• Critical discussion of Tomboulis's approach to the confinement problem