A holographic perspective on the axion quality problem

Peter Cox,Tony Gherghetta,Minh D Nguyen

doi:10.1007/jhep01(2020)188

Abstract

The axion provides a compelling solution to the strong CP problem as well as a candidate for the dark matter of the universe. However, the axion solution relies on the spontaneous breaking of a global U(1)PQ symmetry, which is also explicitly violated by quantum gravity. To preserve the axion solution, gravitational violations of the U(1)PQ symmetry must be suppressed to sufficiently high order. We present a simple, geometric solution of the axion quality problem by modelling the axion with a bulk complex scalar field in a slice of AdS5, where the U(1)PQ symmetry is spontaneously broken in the bulk but explicitly broken on the UV brane. By localising the axion field towards the IR brane, gravitational violations of the PQ symmetry on the UV brane are sufficiently sequestered. This geometric solution is holographically dual to 4D strong dynamics where the global U(1)PQ is an accidental symmetry to sufficiently high order.

Highlights

Background solutionWe restrict to the case where the backreaction of the scalar Φ on the metric can be neglected;2 the equation of motion for the z-dependent scalar vacuum expectation value, η(z), is ∂z A3∂zη − m2ΦA5η = 0, (2.3)with the boundary condition, A dU ∂zη ∓ 2 dη= 0, zUV, zIR (2.4)M53/k, where the upper signs correspond to zUV
Geometric solution of the axion quality problem by modelling the axion with a bulk complex scalar field in a slice of AdS5, where the U(1)P Q symmetry is spontaneously broken in the bulk but explicitly broken on the UV brane
The axion solution requires that the U(1)P Q global symmetry is preserved by quantum gravity to sufficiently high order terms in the Lagrangian

Summary

Background solution

We restrict to the case where the backreaction of the scalar Φ on the metric can be neglected; the equation of motion for the z-dependent scalar vacuum expectation value, η(z), is . The dimensionless coefficients λ and σ are fixed by the boundary conditions in eq (2.4), and the boundary potentials are assumed to have the following form. Note that the linear term in (2.6) explicitly breaks the U(1)P Q symmetry on the UV brane. Using the AdS/CFT correspondence, we can interpret the above 5D setup in terms of a dual strongly interacting 4D conformal field theory (CFT). The presence of the UV and IR branes correspond to explicit and spontaneous breaking of the conformal symmetry respectively, with the latter giving rise to a mass-gapped theory. Σ is identified with a condensate O , and UV with turning on a source for O This source explicitly breaks U(1)P Q, and for ∆ > 4 corresponds to breaking the global symmetry by a Planck-suppressed operator

Pseudoscalar sector

Massless axion

Massive axion

Composite axion models

Conclusion