The Most Irrational Rational Theories

Abstract

We propose a two-parameter family of modular invariant partition functions of two-dimensional conformal field theories (CFTs) holographically dual to pure three-dimensional gravity in anti de Sitter space. Our two parameters control the central charge, and the representation of $SL(2,\mathbb{Z})$. At large central charge, the partition function has a gap to the first nontrivial primary state of $\frac{c}{24}$. As the $SL(2,\mathbb{Z})$ representation dimension gets large, the partition function exhibits some of the qualitative features of an irrational CFT. This, for instance, is captured in the behavior of the spectral form factor. As part of these analyses, we find similar behavior in the minimal model spectral form factor as $c$ approaches $1$.

25 pages plus appendices, 11 figures

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• $\mathcal{N}=2$ Minimal Models: A Holographic Needle in a Symmetric Orbifold Haystack
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• Discreteness and Integrality in Conformal Field Theory
• Spectral form factors of clean and random quantum Ising chains
• Late Time Quantum Chaos of pure states in the SYK model
• Crossing, Modular Averages and $N\leftrightarrow k$ in WZW Models
• No room for minimal monopole dark matter
• Crystalline Spectral Form Factors