High-dimensional sphere packing and the modular bootstrap

Abstract

We carry out a numerical study of the spinless modular bootstrap for conformal field theories with current algebra $U(1{)}^c\times U(1{)}^c$, or equivalently the linear programming bound for sphere packing in $2c$ dimensions. We give a more detailed picture of the behavior for finite $c$ than was previously available, and we extrapolate as $c\to \infty$. Our extrapolation indicates an exponential improvement for sphere packing density bounds in high dimensions. Furthermore, we study when these bounds can be tight. Besides the known cases $c=1/2$, $4$, and $12$ and the conjectured case $c=1$, our calculations numerically rule out sharp bounds for all other $c<90$, by combining the modular bootstrap with linear programming bounds for spherical codes.

arXiv comment48 pages, 19 figures

References in corpus (25)

• Bounding scalar operator dimensions in 4D CFT
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• The sphere packing problem in dimension 24
• The sphere packing problem in dimension 8
• A Universal Inequality for CFT and Quantum Gravity
• Analytic Bounds and Emergence of ${\text{AdS}}_2$ Physics from the Conformal Bootstrap
• Constraints on 2d CFT partition functions
• A tauberian theorem for the conformal bootstrap
• Sphere Packing and Quantum Gravity
• Modular Invariance, Tauberian Theorems, and Microcanonical Entropy
• Fast Conformal Bootstrap and Constraints on 3d Gravity
• Modular Constraints on Calabi-Yau Compactifications
• Tauberian-Cardy formula with spin
• Improved sphere packing lower bounds from Hurwitz lattices
• Beurling-Selberg Extremization and Modular Bootstrap at High Energies
• Sphere packing bounds via spherical codes
• Bounds for State Degeneracies in 2D Conformal Field Theory
• Upper bounds for packings of spheres of several radii
• High Energy Modular Bootstrap, Global Symmetries and Defects
• Bounds on the density of states and the spectral gap in CFT${}_2$
• Fourier interpolation on the real line
• Lessons from the Ramond sector
• The Gaussian core model in high dimensions
• Energy-minimizing error-correcting codes
• Improved Lower Bounds for Kissing Numbers in Dimensions 25 Through 31

Cited by in corpus (26)

• Free partition functions and an averaged holographic duality
• Dispersive CFT Sum Rules
• Bootstrapping Non-Invertible Symmetries
• Harmonic analysis of 2d CFT partition functions
• ${\mathbb{Z}}_N$ Symmetries, Anomalies, and the Modular Bootstrap
• New Developments in the Numerical Conformal Bootstrap
• Adding Flavor to the Narain Ensemble
• Solutions of modular bootstrap constraints from quantum codes
• Comments on the holographic description of Narain theories
• Averaging over moduli in deformed WZW models
• Non-rational Narain CFTs from codes over $F_4$
• Narain CFTs and error-correcting codes on finite fields
• Universality in asymptotic bounds and its saturation in $2$D CFT
• Species scale, worldsheet CFTs and emergent geometry
• Discreteness and Integrality in Conformal Field Theory
• Scalar Modular Bootstrap and Zeros of the Riemann Zeta Function
• Fake Z
• Bootstrapping Closed Hyperbolic Surfaces
• Conformal Bootstrap Deformations
• Honeycomb Layered Frameworks with Metallophilic Bilayers
• Six-dimensional sphere packing and linear programming
• Dynamic Space Packing
• Higher spin wormholes from modular bootstrap
• From sphere packing to Fourier interpolation
• Sign uncertainty principles and low-degree polynomials
• Optimal Narain CFTs from Codes