2002/01/31 by V. P. Gusynin, V. Gusynin, Michio Hashimoto +5 · 7 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.65.116008
published as Phys.Rev. D65 (2002) 116008 · REVTEX4, 38 pages, 18 figures. The abstract is shortened; version to be published in Phys. Rev. D
arxiv created 2002/04/19 · openalex publication_date 2002/06/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate dynamical chiral symmetry breaking in vectorlike gauge theories in D dimensions with D\ensuremath-4 compactified extra dimensions, based on the gap equation (Schwinger-Dyson equation) and the effective potential for the bulk gauge theories within the improved ladder approximation. The nonlocal gauge fixing method is adopted so as to keep the ladder approximation consistent with the Ward-Takahashi identities. Using the one-loop modified minimal subtraction scheme (MS) gauge coupling of the truncated Kaluza-Klein effective theory, which has a nontrivial ultraviolet fixed point g* for the (dimensionless) bulk gauge coupling \ifmmode g\else \g\fi, we find that there exists a critical number of flavors Nfcrit [\ensuremath≃4.2,1.8 for D=6,8 for SU(3) gauge theory]. For Nf>Nfcrit, the dynamical chiral symmetry breaking takes place not only in the ``strong-coupling phase'' (\ifmmode g\else \g\fi>g*) but also in the ``weak-coupling phase'' (\ifmmode g\else \g\fi<g*) when the cutoff is large enough. For Nf<Nfcrit, on the other hand, only the strong-coupling phase is a broken phase and we can formally define a continuum (infinite cutoff) limit, so that the physics is insensitive to the cutoff in this case. We also perform a similar analysis using the one-loop ``effective gauge coupling.'' We find that Nfcrit turns out to be a value similar to that of the MS case, notwithstanding the enhancement of the coupling compared with that of the MS.