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, 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, 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.
Highlights
Since the advent of the AdS/conformal field theories (CFTs) correspondence [1], progress on quantum gravity and on understanding and constructing large families of CFTs have been inextricably linked.A complete solution of a CFT with a large radius gravity dual would likely shed light on many subtle questions about bulk gravitational physics
We pause here to emphasize that any infinite sequence of rational conformal field theory (RCFT) where the least common denominator d amongst states becomes arbitrarily large could in principle exhibit similar features; in this paper, we focus on the Virasoro minimal models as an explicit example
We proposed a family of partition functions for 2d CFTs that we conjecture to be dual to pure AdS3 gravity
Summary
Since the advent of the AdS/CFT correspondence [1], progress on quantum gravity and on understanding and constructing large families of CFTs have been inextricably linked. A spartan approach to this constraint is to look for theories dual to pure gravity, i.e. to attempt to build theories with as large a gap between the vacuum and the state as possible. Witten explored this question for chiral or holomorphically factorized conformal field theories [4]. We borrow technology originally introduced by Bantay and Gannon to describe the modular properties of characters of rational conformal field theories [20] These vector valued modular forms (VVMFs) transform under finite-dimensional representations of the modular group SL(2, Z), and we use this to build candidate partition functions with sparse light spectra. Readers interested in the large c construction can skip to section 3; readers interested the analysis of the spectral form factor for our candidate theories of pure gravity can skip to section 4; readers solely interested in whether or not we cited them can skip to page 32
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