Loading [MathJax]/extensions/Safe.js
SciPost logo

SciPost Submission Page

Fusion rules and structure constants of E-series minimal models

by Rongvoram Nivesvivat, Sylvain Ribault

Submission summary

Authors (as registered SciPost users): Rongvoram Nivesvivat
Submission information
Preprint Link: https://arxiv.org/abs/2502.14295v2  (pdf)
Date submitted: 2025-03-19 08:01
Submitted by: Nivesvivat, Rongvoram
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical

Abstract

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 $c\in (-\infty,1)$, 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 $p,q\to \infty$.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
In refereeing

Login to report or comment