Large Hierarchies from Attractor Vacua

TL;DR

The paper proposes an attractor mechanism for the Higgs mass in a vast landscape of vacua, using a three-form field coupled to the Higgs and brane dynamics to convert the UV-sensitive hierarchy problem into a super-selection problem with an infinite density of vacua near small $m_eta$. A discrete brane-conjugation symmetry makes the brane charge depend on the Higgs field, producing a clustering of vacua around a hierarchically small Higgs VEV, often set by the QCD scale in minimal models. Realistic implementations are laid out via either a quark-condensate second doublet or a heavy second doublet, yielding a viable electroweak scale and predictive Yukawa structures under a $Z_{2N}$ symmetry. Extensions to grand unifications show that the attractor can also address the doublet-triplet splitting problem, while maintaining the core feature of UV-insensitivity and potential testable predictions. The framework connects to string-theory ingredients (three-forms, axions, branes) and offers a novel, largely decoupled route to naturalness that could have observable consequences in flavor structure.

Abstract

We discuss a mechanism through which the multi-vacua theories, such as String Theory, could solve the Hierarchy Problem, without any UV-regulating physics at low energies. Because of symmetry the number density of vacua with a certain hierarchically-small Higgs mass diverges, and is an attractor on the vacuum landscape.The hierarchy problem is solved in two steps. It is first promoted into a problem of the super-selection rule among the infinite number of vacua (analogous to theta-vacua in QCD), that are finely scanned by the Higgs mass. This rule is lifted by heavy branes, which effectively convert the Higgs mass into a dynamical variable. The key point is that a discrete "brane-charge-conjugation" symmetry guarantees that the fineness of the vacuum-scanning is set by the Higgs mass itself. On a resulting landscape in all, but a measure-zero set of vacua the Higgs mass has a common hierarchically-small value. In minimal models this value is controlled by the QCD scale and is of the right magnitude. Although in each particular vacuum there is no visible UV-regulating low energy physics, the realistic models are predictive. For example, we show that in the minimal case the "charge conjugation" symmetry is automatically a family symmetry, and imposes severe restrictions on quark Yukawa matrices.