[Paper Review] Stringy Origin of Discrete R-symmetries

Hans Peter Nilles|arXiv (Cornell University)|May 4, 2017

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper proposes that discrete R-symmetries in supersymmetric particle physics arise naturally from string theory compactifications, where the geometry and field localization in extra dimensions generate these symmetries via string selection rules. The key contribution is showing that R-symmetries—originating from Lorentz invariance in compactified dimensions—naturally solve the μ-problem, suppress proton decay, and lead to hierarchical soft SUSY breaking terms, enabling natural supersymmetry.

ABSTRACT

Discrete symmetries play a crucial role in particle physics. They appear abundantly in string model constructions. We focus here on the case of discrete $R$-symmetries which are intrinsically connected to the Lorentz group in extra dimensions and the appearance of $N$-extended supersymmetry. In that sense, discrete $R$-symmetries can be understood as "fractionally" extended supersymmetry. These symmetries reveal insight about the location of fields in extra dimensions (in particular the Higgs boson). Applications can be found in the solution of the $μ$-problem, suppression of proton decay and the structure of the soft terms of broken supersymmetry.

Motivation & Objective

• To understand the top-down origin of discrete R-symmetries in string-theoretic UV-completions of the MSSM.
• To explain how R-symmetries emerge from the interplay of compact manifold geometry and string selection rules.
• To investigate how field localization in extra dimensions (e.g., on branes or fixed points) determines the structure of R-symmetries.
• To demonstrate that R-symmetries can resolve the μ-problem and stabilize the LSP for dark matter.
• To show that hierarchical soft terms in SUSY breaking arise naturally from sector-dependent R-symmetry and supersymmetry enhancement.

Proposed method

• Analyzes compactified string theories (type IIA, IIB, heterotic) with six extra dimensions to identify discrete symmetries from geometric and topological properties.
• Applies string theory selection rules to derive selection rules for operators, leading to discrete R-symmetries.
• Examines field localization on branes (e.g., 3-branes, 5-branes, 7-branes) and fixed points to determine how R-symmetries are realized in different sectors.
• Uses the interplay between Lorentz invariance in extra dimensions and N-extended supersymmetry to derive R-symmetries as fractional extensions of R-charge symmetry.
• Applies the framework to model-building, showing that R-symmetries protect the μ-term and forbid dangerous dimension-4 proton decay operators.
• Analyzes soft SUSY-breaking terms in different sectors (bulk, twisted, localized) to show hierarchical patterns consistent with mirage mediation and natural SUSY.

Experimental results

Research questions

• RQ1 How do discrete R-symmetries emerge from the geometry and field localization in compactified string theories?
• RQ2 What is the connection between Lorentz invariance in extra dimensions and the emergence of R-symmetries?
• RQ3 How do R-symmetries resolve the μ-problem in the MSSM within a string-theoretic framework?
• RQ4 In what way do R-symmetries suppress proton decay and stabilize the LSP for dark matter?
• RQ5 How do R-symmetries lead to hierarchical soft terms in the context of natural supersymmetry?

Key findings

• Discrete R-symmetries arise as a consequence of string theory selection rules combined with the geometry and field localization in compact extra dimensions.
• R-symmetries are intrinsically linked to the Lorentz group in extra dimensions and the presence of N-extended supersymmetry, suggesting they are fractional extensions of R-charge symmetry.
• The μ-problem is solved because R-symmetries forbid the μ-term at tree level, and its smallness arises from soft breaking via non-perturbative effects.
• Proton decay via dimension-4 operators is forbidden by R-symmetries, and the LSP is stabilized as a dark matter candidate.
• Hierarchical soft SUSY-breaking terms emerge naturally: bulk fields (N=4) have vanishing tree-level soft terms, while localized fields (N=1) have large masses, leading to a mirage-mediation-like pattern.
• Extended R-symmetries provide UV protection, reducing fine-tuning and enabling natural supersymmetry with only a few superpartners in the TeV range.