2006/09/28 by M. A. L. Capri, V. E. R. Lemes, R. F. Sobreiro +3
Mathematics · Physics and Astronomy · #Abelian group #Black Holes and Theoretical Physics #Combinatorics #Coupling constant #Gauge theory #Mathematical analysis #Mathematical physics #Mathematics #Multiplicative function #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Renormalization #hep-lat #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.74.105007
published as Phys.Rev.D74:105007,2006 · 31 pages
arxiv created 2006/09/28 · openalex publication_date 2006/11/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We pursue the study of SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge by taking into account the effects of the Gribov horizon. The Gribov approximation, previously introduced in [M. A. L. Capri, V. E. R. Lemes, R. F. Sobreiro, S. P. Sorella, and R. Thibes, Phys. Rev. D 72, 085021 (2005).], is improved through the introduction of the horizon function, which is constructed under the requirements of localizability and renormalizability. By following Zwanziger's treatment of the horizon function in the Landau gauge, we prove that, when cast in local form, the horizon term of the maximal Abelian gauge leads to a quantized theory which enjoys multiplicative renormalizability, a feature which is established to all orders by means of the algebraic renormalization. Furthermore, it turns out that the horizon term is compatible with the local residual U(1) Ward identity, typical of the maximal Abelian gauge, which is easily derived. As a consequence, the nonrenormalization theorem, ZgZA1/2=1, relating the renormalization factors of the gauge coupling constant Zg and of the diagonal gluon field ZA, still holds in the presence of the Gribov horizon. Finally, we notice that a generalized dimension two gluon operator can be also introduced. It is BRST invariant on-shell, a property which ensures its multiplicative renormalizability. Its anomalous dimension is not an independent parameter of the theory, being obtained from the renormalization factors of the gauge coupling constant and of the diagonal antighost field.