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Reproducing Standard Model fermion masses and mixing in string theory: A heterotic line bundle study

Andrei Constantin1,2,*, Lucas T.-Y. Leung2,†, Andre Lukas2,‡, and Luca A. Nutricati2,§

  • 1School of Mathematics, University of Birmingham, Watson Building, Edgbaston, Birmingham B15 2TT, United Kingdom
  • 2Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom

  • *Contact author: andrei.constantin@physics.ox.ac.uk
  • †Contact author: lucas.leung@physics.ox.ac.uk
  • ‡Contact author: andre.lukas@physics.ox.ac.uk
  • §Contact author: luca.nutricati@physics.ox.ac.uk
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Phys. Rev. D 113, 046005 – Published 9 February, 2026

DOI: https://doi.org/10.1103/fbdz-t73z

Abstract

Deriving the Yukawa couplings and the resulting fermion masses and mixing angles of the Standard Model (SM) from a more fundamental theory remains one of the central outstanding problems in theoretical high-energy physics. It has long been recognized that string theory provides a framework within which this question can, at least in principle, be addressed. While substantial progress has been made in studying flavor physics in string compactifications over the past few decades, a concrete string construction that reproduces the full set of observed SM flavor parameters remains unknown. Here, we take a significant step in this direction by identifying two explicit E8×E8 heterotic string models compactified on a Calabi-Yau threefold with Abelian, holomorphic, and polystable vector bundles with minimal supersymmetric (MS) SM spectrum. Subject to reasonable assumptions about the moduli, we show that these models reproduce the correct values of the quark and charged lepton masses, as well as the quark mixing parameters, at some point in their moduli spaces. The resulting four-dimensional theories are N=1 supersymmetric, contain no exotic fields, and realize a μ-term suppressed to the electroweak scale. While the issues of moduli stabilization and supersymmetry breaking are not addressed here; our main result constitutes a proof of principle: There exist choices of topology and moduli within heterotic string compactifications which allow for an MSSM spectrum with the correct flavor parameters.

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Phys. Rev. D 113, 046005– Published 9 February, 2026
  • Received 10 September 2025
  • Accepted 15 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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