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The Holographic QCD Axion in Five Dimensions

Csaba Csáki, Eric Kuflik, Wei Xue, Taewook Youn

Abstract

We present a holographic construction of the QCD axion based on a warped 5D model. A key ingredient of our setup is the introduction of a bulk scalar field $θ$, which is holographically dual to the topological operator of QCD. This makes the relation among the axion, the $η'$, and the anomalies transparent. We identify the bulk modes corresponding to the $η'$ and axion states, and show that an adjustment analogous to that of the usual 4D axion takes place. We identify the origin of the axion quality problem in this framework and show that a large degree of axion compositeness is needed to solve it. We also find that, in the limit of a high quality axion, the physical axion state is predominantly contained in the bulk gauge field.

The Holographic QCD Axion in Five Dimensions

Abstract

We present a holographic construction of the QCD axion based on a warped 5D model. A key ingredient of our setup is the introduction of a bulk scalar field , which is holographically dual to the topological operator of QCD. This makes the relation among the axion, the , and the anomalies transparent. We identify the bulk modes corresponding to the and axion states, and show that an adjustment analogous to that of the usual 4D axion takes place. We identify the origin of the axion quality problem in this framework and show that a large degree of axion compositeness is needed to solve it. We also find that, in the limit of a high quality axion, the physical axion state is predominantly contained in the bulk gauge field.

Paper Structure

This paper contains 14 sections, 64 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The 5D Action
  3. The axion and $\eta'$ modes and the strong CP problem
  4. The axion quality problem and the composition of the axion
  5. The Holographic PQ mechanism
  6. Conclusion
  7. Acknowledgments
  8. QCD Matching
  9. Bulk Gauge Coupling ($g_\theta^2$)
  10. Anomaly Coefficients ($\kappa_A, \kappa_B$)
  11. Gauge Couplings ($e_A^2, e_B^2$)
  12. $U(1)$ Charges ($q_A, q_B$)
  13. $R_\xi$ Gauge
  14. Zero Mode Profiles

Figures (2)

  • Figure 1: Illustration of the brane configuration: the IR brane sets the QCD scale, while the PQ brane sets the scale for the axion physics.
  • Figure 2: $\Delta\overline{\theta}$ against $n\Delta_Y$ for $n = N_{\mathrm{PQ}}$, $v_Y z_{\mathrm{PQ}} = 1$ and different $\epsilon_{\cancel{\mathrm{PQ}}}$ values: $0.1 \;\hbox{eV}$ ($m_\nu$), $3\;\hbox{MeV}$ ($m_q$), $10^{12}\;\hbox{GeV}$ ($\Lambda_{\mathrm{PQ}}$), and $1.22\times10^{19}\;\hbox{GeV}$ ($M_{pl}$).