TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.5.163
TI  - Fusion rules and structure constants of E-series minimal models
PY  - 2025/05/21
UR  - https://scipost.org/SciPostPhys.18.5.163
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 5
SP  - 163
A1  - Nivesvivat, Rongvoram
AU  - Ribault, Sylvain
AB  - In the ADE classification of Virasoro minimal models, the E-series is the sparsest: their central charges $c=1-6\frac{(p-q)^2}{pq}$ are not dense in the half-line $c∈ (-∞,1)$, due to $q=12,18,30$ taking only 3 values — the Coxeter numbers of $E_6, E_7, E_8$. The E-series is also the least well understood, with few known results beyond the spectrum. Here, we use a semi-analytic bootstrap approach for numerically computing 4-point correlation functions. We deduce non-chiral fusion rules, i.e. which 3-point structure constants vanish. These vanishings can be explained by constraints from null vectors, interchiral symmetry, simple currents, extended symmetries, permutations, and parity, except in one case for $q=30$. We conjecture that structure constants are given by a universal expression built from the double Gamma function, times polynomial functions of $\cos(\pi\frac{p}{q})$ with values in $\mathbb{Q}\big(\cos(\frac{\pi}{q})\big)$, which we work out explicitly for $q=12$. We speculate on generalizing E-series minimal models to generic integer values of $q$, and recovering loop CFTs as $p,q\to ∞$.
ER  -

@Article{10.21468/SciPostPhys.18.5.163,
	title={{Fusion rules and structure constants of E-series minimal models}},
	author={Rongvoram Nivesvivat and Sylvain Ribault},
	journal={SciPost Phys.},
	volume={18},
	pages={163},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.5.163},
	url={https://scipost.org/10.21468/SciPostPhys.18.5.163},
}