Solutions of modular bootstrap constraints from quantum codes

Abstract

Modular invariance imposes rigid constrains on the partition functions of two-dimensional conformal field theories. Many fundamental results follow strictly from modular invariance, giving rise to the numerical modular bootstrap program. Here we report a way to assign to a particular family of quantum error correcting codes a family of "code CFTs" CFTs", which forms a subset of the space of Narain CFTs. This correspondence reduces modular invariance of the 2d CFT partition function to a few simple algebraic relations obeyed by a multivariate polynomial characterizing the corresponding code. Using this relation we construct many explicit examples of physically distinct isospectral theories, as well as many examples of nonholomorphic functions, which satisfy all basic properties of the 2d CFT partition function, yet are not associated with any known CFT.

Published version with supplemental material included. 7 pages, 1 figure

References in corpus (5)

• Three-Dimensional Gravity Revisited
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Fast Conformal Bootstrap and Constraints on 3d Gravity
• Quantum stabilizer codes, lattices, and CFTs
• Classification of RCFT from Holomorphic Modular Bootstrap: A Status Report

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• Narain CFTs and Quantum Codes at Higher Genus
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• Classical Codes and Chiral CFTs at Higher Genus
• Holographic description of Narain CFTs and their code-based ensembles
• Relation between spectra of Narain CFTs and properties of associated boolean functions
• Fake Z
• Landauer's principle in Qubit-Cavity quantum field theory Interaction in Vacuum and Thermal States
• Global Symmetries, Code Ensembles, and Sums Over Geometries
• Wobbling kinks and shape mode interactions in a coupled two-component ${\varphi }^4$ theory
• Fermionic CFTs from topological boundaries in abelian Chern-Simons theories
• Optimal Narain CFTs from Codes
• Code CFTs and Topological Matter
• Algebraic constructions of code lattices in Narain conformal field theories