# The Most Irrational Rational Theories

## TL;DR

This paper introduces a two-parameter family of modular invariant partition functions for 2D CFTs, revealing features akin to irrational CFTs and analyzing spectral form factors near minimal models.

## Contribution

It constructs a novel class of partition functions with adjustable parameters, connecting holographic duals of pure 3D gravity to irrational CFT characteristics.

## Key findings

- Partition functions exhibit a gap to the first primary state at large central charge.
- Spectral form factor behavior mimics that of irrational CFTs as parameters vary.
- Similar spectral behavior observed in minimal models near c=1.

## 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 $1$.