Abstract
Modular invariance imposes rigid constraints on the partition functions of two-dimensional conformal field theories (CFTs). Many fundamental results follow strictly from modular invariance and unitarity, giving rise to the numerical modular bootstrap program. Here we report on a way to relate a particular family of quantum error correcting codes to a family of "code 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 correspondence, we construct many explicit examples of physically distinct isospectral theories, as well as many examples of nonholomorphic functions, which satisfy all the basic properties of a 2D CFT partition function, yet are not associated with any known CFT.
| Original language | English |
|---|---|
| Article number | 161602 |
| Journal | Physical Review Letters |
| Volume | 126 |
| Issue number | 16 |
| DOIs | |
| State | Published - Apr 21 2021 |
Bibliographical note
Publisher Copyright:© 2021 authors.
Funding
We thank Petr Kravchuk and Xi Yin for discussions. A.\u2009D. is supported by the National Science Foundation under Grant No. PHY-2013812.
| Funders | Funder number |
|---|---|
| U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China | PHY-2013812 |
ASJC Scopus subject areas
- General Physics and Astronomy