[Paper Review] F-Theory, GUTs and Chiral Matter

Martijn Wijnholt|ArXiv.org|Sep 23, 2008

Black Holes and Theoretical Physics17 references15 citations

TL;DR

This paper proposes F-theory compactifications on elliptically fibered Calabi-Yau fourfolds as a viable framework for constructing realistic Grand Unified Theories (GUTs) with chiral matter, leveraging flux-induced gauge symmetry breaking and localized zero modes to suppress proton decay. It demonstrates that F-theory can realize exceptional gauge groups like E8, SU(5), and SO(10), enabling non-perturbative Yukawa couplings essential for the top quark mass, while suppressing dangerous dimension-five and four operators via wavefunction localization.

ABSTRACT

This is a write-up of a two hour talk at the Simons workshop. It contains an elementary introduction to F-theory and may be useful for people new to the subject.

Motivation & Objective

• To construct realistic GUT models in F-theory that incorporate chiral matter and gauge unification, addressing limitations of perturbative D-brane models.
• To resolve the challenge of realizing non-perturbative Yukawa couplings—such as the SU(5) epsilon tensor coupling—required for the top quark mass.
• To suppress proton decay by leveraging wavefunction localization in extra dimensions, particularly for dimension-five and four operators.
• To demonstrate that F-theory provides a consistent framework for local model building with built-in unification, avoiding the landscape problem of generic brane models.
• To show that F-theory models can achieve gauge coupling unification and viable proton decay rates consistent with experimental bounds.

Proposed method

• Utilize F-theory compactifications on Calabi-Yau fourfolds with elliptic fibrations to realize non-perturbative gauge groups such as E8, SU(5), and SO(10).
• Implement fluxes on the compactification manifold to break the GUT group down to the Standard Model gauge group, preserving the necessary chiral spectrum.
• Apply wavefunction localization in the extra dimensions to suppress dimension-five and four proton decay operators mediated by Higgsino and Kaluza-Klein modes.
• Compute leading corrections to gauge couplings using Ray-Singer torsion and loop effects from Kaluza-Klein modes, estimating them at a few percent with varying signs.
• Analyze the parametric dependence of dimension-six proton decay amplitudes via the Green’s function on the compactification space, finding a mild logarithmic enhancement over 4D GUT models.
• Use the F-theory/heterotic duality to infer the structure of chiral matter and couplings before a full algebraic geometry construction was available.

Experimental results

Research questions

• RQ1 Can F-theory compactifications realize non-perturbative Yukawa couplings necessary for the top quark mass, such as the epsilon tensor in SU(5) GUTs?
• RQ2 How can proton decay be suppressed in F-theory GUT models, particularly the dangerous dimension-five and four operators?
• RQ3 What role do fluxes and wavefunction localization play in breaking the GUT group and suppressing gauge-mediated proton decay?
• RQ4 Can F-theory models achieve gauge coupling unification with corrections of order a few percent, consistent with low-energy data?
• RQ5 What distinguishes F-theory GUTs from perturbative D-brane models in terms of phenomenological viability and predictive power?

Key findings

• F-theory provides a consistent framework for constructing GUTs with exceptional gauge groups like E8, SU(5), and SO(10), overcoming the limitations of perturbative D-brane models.
• Non-perturbative Yukawa couplings, such as the SU(5) epsilon tensor coupling for the top quark, are naturally realized in F-theory due to the underlying E8 gauge group.
• Proton decay from dimension-five operators is suppressed via wavefunction localization of chiral zero modes in the extra dimensions, particularly for Higgsino and Kaluza-Klein modes.
• The leading corrections to gauge couplings are estimated at a few percent and come with varying signs, consistent with observed values at the GUT scale.
• Dimension-six proton decay amplitudes receive a mild logarithmic enhancement in F-theory compared to 4D GUTs, scaling as ∼αGUT log αGUT⁻¹ / M_GUT², but remain phenomenologically viable.
• F-theory models offer a new class of local, predictive GUTs with built-in unification, making them strong candidates for realistic model building beyond the heterotic string.