Solutions of modular bootstrap constraints from quantum codes [article]

Anatoly Dymarsky, Alfred Shapere
2020 arXiv   pre-print
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" -- a subset in the space of Narain CFTs. This relation reduces modular invariance of the 2d CFT partition function to simple algebraic relations at
more » ... e level of 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 non-holomorphic functions, which satisfy all basic properties of the 2d CFT partition function, yet are not associated with any known theory.
arXiv:2009.01236v1 fatcat:6mic6l6225cd7j6huvywz4j6ni