Relation between spectra of Narain CFTs and properties of associated boolean functions

Abstract

Recently, the construction of Narain CFT from a certain class of quantum error correcting codes has been discovered. In particular, the spectral gap of Narain CFT corresponds to the binary distance of the code, not the genuine Hamming distance. In this paper, we show that the binary distance is identical to the so-called EPC distance of the boolean function uniquely associated with the quantum code. Therefore, seeking Narain CFT with high spectral gap is equivalent to getting a boolean function with high EPC distance. Furthermore, this problem can be addressed by finding lower Peak-to-Average Power ratio (PAR) with respect to the binary truth table of the boolean function. Though this is neither sufficient nor necessary condition for high EPC distance, we construct some examples of relatively high EPC distances referring to the constructions for lower PAR. We also see that codes with high distance are related to induced graphs with low independence numbers.

27 pages, 1 figure

References in corpus (6)

• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Solutions of modular bootstrap constraints from quantum codes
• Comments on the holographic description of Narain theories
• Non-rational Narain CFTs from codes over $F_4$
• Narain CFTs and error-correcting codes on finite fields
• Quantum stabilizer codes, lattices, and CFTs

Cited by in corpus (5)

• Fermionic CFTs from classical codes over finite fields
• Narain CFTs and Quantum Codes at Higher Genus
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Fermionic CFTs from topological boundaries in abelian Chern-Simons theories
• Optimal Narain CFTs from Codes