Abstract
We investigate nonlinear extensions of the holographic soft wall model proposed by Karch et al. [Phys. Rev. D 74, 015005 (2006)] with a positive quadratic dilaton. We consider a Higgs potential for the tachyonic field that brings a more natural realization of chiral symmetry breaking in the infrared regime. Utilizing the $\mathrm{AdS}/\mathrm{CFT}$ dictionary and holographic renormalization, we find the chiral condensate as a function of the quark mass. The nonlinearity of the Higgs potential leads to a nonlinear relation between the chiral condensate and the quark mass. Solving the effective Schr\"odinger equations for the field perturbations, we estimate meson masses and decay constants and evaluate their dependence on the quark mass. In the axial and pseudoscalar sector we find an interesting behavior for the decay constants as the quark mass increases. We also investigate the effect of a five-dimensional running mass for the tachyonic field. We conclude that nonlinear soft wall models with a Higgs potential for the tachyon and a positive quadratic dilaton do not provide spontaneous symmetry breaking in the chiral limit.
Highlights
The dynamical breaking of chiral symmetry in quantum chromodynamics (QCD) is a fascinating phenomenon that occurs in the strongly coupled regime
We conclude that nonlinear soft wall models with a Higgs potential for the tachyon and a positive quadratic dilaton do not provide spontaneous symmetry breaking in the chiral limit
In this work we investigated a nonlinear realization for chiral symmetry breaking in soft wall models based on a Higgs potential
Summary
The dynamical breaking of chiral symmetry in quantum chromodynamics (QCD) is a fascinating phenomenon that occurs in the strongly coupled (nonperturbative) regime. The chiral condensate hqqi is proportional to the quark mass mq just as a consequence of the linearity of the tachyonic field equation This implies, in particular, that taking the chiral limit mq → 0 in the soft wall model does not lead to spontaneous chiral symmetry breaking (the chiral condensate vanishes). In this work we perform a systematic analysis of the background and field perturbations for nonlinear soft wall models based on a positive quadratic dilaton Φ and a Higgs potential for the tachyonic field X. Our approach was partially inspired by the holographic QCD model of [10], where chiral symmetry breaking maps to tachyon condensation in string theory. Appendix B briefly reviews the holographic model of [11], while Appendix C describes some complementary numerical results
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