The Self‐Tuning of the Cosmological Constant and the Holographic Relaxion

Abstract

We propose a brane‐world setup based on gauge/gravity duality that permits the simultaneous realisation of self‐tuning of the cosmological constant and a stabilisation of the electroweak hierarchy. The Standard Model dynamics including the Higgs sector is confined to a flat 4‐dimensional brane, embedded in a 5‐dimensional bulk whose dynamics is governed by Einstein‐dilaton‐axion gravity. The inclusion of a dynamical bulk axion is new compared to previous implementations of the self‐tuning mechanism. Because of the presence of the axion, the model generically exhibits a multitude of static solutions, with different values for the equilibrium position for the brane. Under mild assumptions regarding the dependence of brane parameters on bulk fields, a number of these solutions exhibit electroweak symmetry breaking with a small Higgs mass as compared to the cutoff‐scale of the brane theory. The realisation of self‐tuning of the cosmological constant is generic and as efficient as in previous constructions without a bulk axion. Vacua with a small Higgs mass can sometimes be found, regardless of whether the brane theory depends explicitly on the bulk axion. Because it is expected on general principles that the brane action will depend on the axion, the generation of solutions with a hierarchy is a robust feature.

Global symmetries, hidden sectors and emergent (dark) vector interactions

“…• In the holographic context, the coupling controlling the interactions of the emergent vector is naturally weak, in the large N limit. The same applies to the bulk contributions to its mass, similarly to what happens to gravitons in a similar setting, [53,54].…”

“…Finally, the boundary conditions for the bulk action are Neumann. It should be noted that what we have here is a close analogue of the DGP mechanism, [61], with two differences: here we have a vector field and also the bulk data are non-trivial as in the setup of [53,54].…”

“…The general solution can be written in terms of the bulk propagator G 0 with Neumann boundary conditions at the boundary as follows 17 [53,54]…”

“…The general structure of the bulk propagator G 0 is derived in appendix G and follows a similar structure of the scalar bulk propagator, [53,54]. Similar to our manipulations in the appendix, we perform a scale transformation in order to bring the induced metric on the brane to be η µν .…”

Holographic Theories at Finite θ‐Angle, CP‐Violation, Glueball Spectra and Strong‐Coupling Instabilities

“…Composite axions may also be instrumental in connecting the self‐tuning mechanism of the cosmological constant, [ 19 ] to the gauge hierarchy problem. [ 20 ]…”