Grand Unified Theories require complex representations to account for observed fermion chiral anomalies.
Evidence from high-energy physics and string theory supports the requirement that Grand Unified Theories must employ complex representations and specific anomaly cancellation mechanisms to remain consistent.
Papers [3], [5], and [10] discuss how anomaly cancellation in Grand Unified Theories and string compactifications relies on specific complex representations and advanced mathematical structures such as sheaf cohomologies and Chow groups. There are no papers contradicting the claim.
Martin Bies. Cohomologies of coherent sheaves and massless spectra in F-theory. 2018. https://doi.org/10.11588/heidok.00024045
Discusses how line bundles and hypercharge fluxes in F-theory Grand Unified Theories require sophisticated cohomological methods like Chow groups to account for anomaly cancellation and zero mode counting.
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L. Chang, C. Soo. Chiral fermions, Gravity and GUTs. 1994
Demonstrates that global gravitational and gauge anomalies impose strict algebraic constraints on Grand Unified Theories, selecting specific fundamental representations such as the 16-dimensional Weyl representation of SO(10).
Bhattacharjee D, Samal P, Bhattacharya S. Geometric Structure and Renormalization Group Flow in Chiral Yang–Mills–Higgs Theory. 2026. https://doi.org/10.20944/preprints202602.2022.v1
Notes that ultraviolet embeddings and Grand Unified Theories require careful consideration of chiral fermion representations and complex representations to ensure anomaly cancellation.
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