Abstract
The singlet pseudoscalar sector of light mesons is investigated in the soft-wall model, a bottom-up approach to the AdS/QCD correspondence. The $\eta^\prime$ mass results from the mixing among the fields dual to the axial current, pseudoscalar current and the $G\tilde G$ operator. The topological susceptibility is computed for any quark mass, and the Witten-Veneziano relation is obtained in the large $N_c$ limit.
Highlights
In QCD the absence of a singlet pseudo-Goldostone boson is the well-known Uð1ÞA problem
In the past there have been some discussions on the way the Goldstone boson receives a mass as a result of the anomaly. ’t Hooft proposed that the violation of Uð1ÞA is realized by instanton configurations that explicitly break the symmetry and contribute to the η0 mass [3,4]
We have found that the mixing of singlet states with pseudoscalar glueballs can explain the large mass of the η0
Summary
In QCD the absence of a singlet pseudo-Goldostone boson is the well-known Uð1ÞA problem. Term for the gauge field dual to the Uð1ÞR current is generated by a 2-form in the gravity theory which is not invariant under Uð1ÞR On these bases, studies of the Uð1ÞA problem in top-down [17,18,19,20,21,22] and bottom-up models [23,24,25,26] have been proposed. The result involving the axion a, i.e., the field sourced by θ that couples to G ∧ G on the boundary, is gauge invariant if the following transformations of the 5d fields under Uð1ÞA are assumed: η0 → η0 − α; ð5Þ φ0 → φ0 − α; ð6Þ a → a − Vaα; ð7Þ where α is the gauge parameter, and VaðzÞ is a potential term depending on the tachyon vacuum expectation value vqðzÞ, such that Va → 1 as z → 0 and Va → 0 for vqðzÞ → ∞.
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