
TL;DR
This paper investigates the distinction between genuine Narain CFT partition functions and fake solutions that satisfy modular invariance and positivity but do not correspond to actual CFTs, highlighting limitations of the modular bootstrap.
Contribution
The authors identify and analyze fake polynomials that meet bootstrap constraints but do not correspond to real Narain CFTs, demonstrating limitations of the bootstrap approach.
Findings
Six fake polynomials are shown not to be Narain CFT partition functions.
Four of the fake polynomials are not associated with any unitary 2D CFT.
The analysis reveals that not all bootstrap solutions correspond to actual CFTs.
Abstract
Recently introduced connections between quantum codes and Narain CFTs provide a simple ansatz to express a modular-invariant function in terms of a multivariate polynomial satisfying certain additional properties. These properties include algebraic identities, which ensure modular invariance of , and positivity and integrality of coefficients, which imply positivity and integrality of the character expansion of . Such polynomials come naturally from codes, in the sense that each code of a certain type gives rise to the so-called enumerator polynomial, which automatically satisfies all necessary properties, while the resulting is the partition function of the code CFT -- the Narain theory unambiguously constructed from the code. Yet there are also ``fake''…
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Coding theory and cryptography
