[Paper Review] In Search of the (Minimal Supersymmetric) Standard Model String

Gerald Cleaver|ArXiv.org|Mar 2, 2007

Black Holes and Theoretical Physics37 references3 citations

TL;DR

This paper reviews the development of string-derived Minimal Supersymmetric Standard Model (MSSM) constructions, focusing on the first heterotic free fermionic model with exactly the MSSM spectrum—three generations of matter, a single Higgs pair, and no exotic states. It demonstrates how vacuum expectation values from anomaly cancellation generate mass hierarchy and a physical Higgs, while supersymmetry breaking arises via hidden sector condensates, marking a foundational step toward realizing the MSSM in string theory.

ABSTRACT

This paper summarizes several developments in string-derived (Minimal Supersymmetric) Standard Models. Part one reviews the first string model containing solely the three generations of the Minimal Supersymmetric Standard Model and a single pair of Higgs as the matter in the observable sector of the low energy effective field theory. This model was constructed by Cleaver, Faraggi, and Nanopoulos in the Z_2 x Z_2 free fermionic formulation of weak coupled heterotic strings. Part two examines a representative collection of string/brane-derived MSSMs that followed. These additional models were obtained from various construction methods, including weak coupled Z_6 heterotic orbifolds, strong coupled heterotic on elliptically fibered Calabi-Yau's, Type IIB orientifolds with magnetic charged branes, and Type IIA orientifolds with intersecting branes (duals of the Type IIB). Phenomenology of the models is compared. To appear in String Theory Research Progress, Ferenc N. Balogh, editor., (ISBN 978-1-60456-075-6), Nova Science Publishers, Inc.}

Motivation & Objective

• To identify and construct a string theory vacuum that reproduces the exact matter content of the Minimal Supersymmetric Standard Model (MSSM), including three generations and a single Higgs pair, without exotic MSSM-charged states.
• To demonstrate that the MSSM can emerge as a low-energy effective field theory from a consistent string compactification, satisfying key phenomenological constraints such as gauge coupling unification and proton stability.
• To explore the role of hidden sector dynamics and anomaly cancellation mechanisms in generating realistic mass hierarchies and supersymmetry breaking with testable predictions.
• To compare diverse string construction methods—free fermionic models, orbifolds, Calabi-Yau compactifications, and brane configurations—for their ability to yield viable MSSM-like models.
• To assess progress toward realizing the MSSM within the string landscape, particularly in light of cosmological constant stabilization and moduli stabilization.

Proposed method

• Construction of a weakly coupled heterotic string model in the free fermionic formulation on a T⁶/(Z₂×Z₂) orbifold, using a NAHE-based GSO projection to break E₈×E₈ gauge symmetry down to the MSSM gauge group.
• Implementation of Abelian anomaly cancellation via the Green-Schwarz-Dine-Seiberg-Witten mechanism, which induces vacuum expectation values (VEVs) on flat directions that break the gauge group to SU(3)C×SU(2)L×U(1)Y.
• Use of off-diagonal terms in the Higgs mass matrix to mix Higgs components, resulting in a physical Higgs state that is a superposition of generations, enabling large mass hierarchy with low-order couplings.
• Incorporation of hidden sector condensates to generate non-perturbative supersymmetry breaking, providing a mechanism for generating gaugino and scalar masses.
• Analysis of alternative constructions including Z₆' heterotic orbifolds, elliptically fibered Calabi-Yau compactifications, Type IIB orientifolds with magnetic branes, and Type IIA intersecting brane models to compare phenomenological features.
• Evaluation of moduli stabilization and cosmological constant generation via anti-brane uplift in brane-based models, aiming for metastable de Sitter vacua.

Experimental results

Research questions

• RQ1 Can a string compactification produce a low-energy effective theory with exactly the MSSM gauge group, three generations of matter, and a single pair of Higgs bosons, without any exotic MSSM-charged states?
• RQ2 How do vacuum expectation values from anomaly cancellation mechanisms generate the observed mass hierarchy and correct electroweak symmetry breaking in MSSM-like models?
• RQ3 What mechanisms in string compactifications can lead to viable non-perturbative supersymmetry breaking with testable mass spectra?
• RQ4 How do different string construction methods—free fermionic models, orbifolds, Calabi-Yau compactifications, and brane configurations—compare in their ability to reproduce MSSM phenomenology?
• RQ5 Can string models achieve a cosmological constant consistent with observations, particularly through anti-brane uplift in brane-based constructions?

Key findings

• The first string model with exactly the MSSM spectrum—three generations, a single Higgs pair, and no exotic states—was constructed in the weakly coupled heterotic free fermionic formulation on T⁶/(Z₂×Z₂), marking a foundational milestone in string phenomenology.
• Generational mass hierarchy arises naturally from vacuum expectation values of scalar fields induced by Abelian anomaly cancellation, even with low-order couplings, allowing for realistic fermion masses.
• The physical Higgs boson is a mixed state of multiple Higgs components, with relative weights differing by orders of magnitude, enabling a large mass hierarchy without fine-tuning.
• Supersymmetry breaking is realized via hidden sector condensates, providing a non-perturbative mechanism that yields testable predictions for gaugino and scalar masses.
• Subsequent models using Z₆' orbifolds, elliptically fibered Calabi-Yau manifolds, and Type IIA/IIB brane configurations confirmed the importance of anomalous U(1) symmetries and flat direction VEVs in achieving gauge symmetry breaking and Higgs mass generation.
• Stable anti-de Sitter vacua with MSSM-like spectra were constructed in brane-based models, and uplifting via anti-branes successfully generated metastable de Sitter vacua with a cosmological constant at the observed scale.