A localisation bound for Standard-Model representations in heterotic orbifolds
Abstract
In heterotic string compactifications on toroidal orbifolds, the massless states at a twisted fixed point are constrained by the evenness of the sixteen-dimensional gauge lattice. We show that two massless left-chiral states in the same Standard-Model representation, built on the same constructing space-group element and distinct modulo the Weyl group of SU(3)c× SU(2)L, must satisfy √R+√(R')≥√2, where R is the squared length of the part of a state's gauge momentum orthogonal to the Standard-Model Cartan directions. Without left-moving oscillator excitations this reads R≥ 1/2. When R<1, n such states, pairwise distinct in the same sense, carry the weights of the fundamental representation of a local SU(n) commuting with the Standard Model, and n≤ 1/(1−R). Since the representation fixes the projected length (at the canonical hypercharge normalisation, 6/5 for the 10-like Q, uc, ec and 4/5 for the 5bar-like dc and lepton doublet), the bound becomes a condition on the sector: a repeated 10-like representation requires a massless budget of at least 17/20, a repeated 5bar-like one at least 13/20. In the complete massless spectra of 16,138 models from two orbifold catalogues the multiplicity ceiling is reached at four values of R. We exhibit an explicit model on T6/(Z3× Z6) whose budget clears the higher threshold and carries a repeated 10-like representation at the multiplicity the bound permits. For the Standard Model embedded through SU(5) in one E8 factor we show that, for that geometry and budget, exactly two inequivalent order-six shift classes admit such a doubling, and among the embeddings over them with the Standard Model intact we find none with three net generations of Q, uc and ec at once.
Related
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- Enhanced Standard Model bound on charm CP violation from QCD penguins
- Heterotic moduli, the double extension and the alpha'^2 metric
BibTeX
@misc{ardakanian2026localisation,
title = {{A localisation bound for Standard-Model representations in heterotic orbifolds}},
author = {Navid Ardakanian},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31873},
eprint = {2610.31873},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31873},
}
RIS
TY - UNPB
TI - A localisation bound for Standard-Model representations in heterotic orbifolds
AU - Navid Ardakanian
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31873
UR - https://arxiv.org/abs/2610.31873
AB - In heterotic string compactifications on toroidal orbifolds, the massless states at a twisted fixed point are constrained by the evenness of the sixteen-dimensional gauge lattice. We show that two massless left-chiral states in the same Standard-Model representation, built on the same constructing space-group element and distinct modulo the Weyl group of SU(3)_c× SU(2)_L, must satisfy √R+√(R')≥√2, where R is the squared length of the part of a state's gauge momentum orthogonal to the Standard-Model Cartan directions. Without left-moving oscillator excitations this reads R≥ 1/2. When R<1, n such states, pairwise distinct in the same sense, carry the weights of the fundamental representation of a local SU(n) commuting with the Standard Model, and n≤ 1/(1−R). Since the representation fixes the projected length (at the canonical hypercharge normalisation, 6/5 for the 10-like Q, u^c, e^c and 4/5 for the 5bar-like d^c and lepton doublet), the bound becomes a condition on the sector: a repeated 10-like representation requires a massless budget of at least 17/20, a repeated 5bar-like one at least 13/20. In the complete massless spectra of 16,138 models from two orbifold catalogues the multiplicity ceiling is reached at four values of R. We exhibit an explicit model on T^6/(Z_3× Z_6) whose budget clears the higher threshold and carries a repeated 10-like representation at the multiplicity the bound permits. For the Standard Model embedded through SU(5) in one E_8 factor we show that, for that geometry and budget, exactly two inequivalent order-six shift classes admit such a doubling, and among the embeddings over them with the Standard Model intact we find none with three net generations of Q, u^c and e^c at once.
ER -