Dynamical chiral symmetry breaking in gauge theories with extra dimensions

Abstract

We investigate dynamical chiral symmetry breaking in vector-like gauge theories in $D$ dimensions with ($D-4$) 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 non-local gauge fixing method is adopted so as to keep the ladder approximation consistent with the Ward-Takahashi identities. Using the one-loop $\overline{\mathrm{MS}}$ gauge coupling of the truncated KK effective theory which has a nontrivial ultraviolet fixed point (UV-FP) $g_{\ast }$ for the (dimensionless) bulk gauge coupling $\hat{g}$, we find that there exists a critical number of flavors, $N_f^{\mathrm{crit}}$ ($\simeq 4.2,1.8$ for $D=6,8$ for SU(3) gauge theory): For $N_f>N_f^{\mathrm{crit}}$, the dynamical chiral symmetry breaking takes place not only in the ``strong-coupling phase'' ($\hat{g}>g_{\ast }$) but also in the ``weak-coupling phase'' ($\hat{g}<g_{\ast }$) when the cutoff is large enough. For $N_f<N_f^{\mathrm{crit}}$, 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 the $N_f^{\mathrm{crit}}$ turns out to be a value similar to that of the $\overline{\mathrm{MS}}$ case, notwithstanding the enhancement of the coupling compared with that of the $\overline{\mathrm{MS}}$.

arXiv commentREVTEX4, 38 pages, 18 figures. The abstract is shortened; version to be published in Phys. Rev. D

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