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"Quantum codes, CFTs, and defects", Matthew Buican, Anatoly Dymarsky, Rajath Radhakrishnan, 2023

Reviewed September 13, 2023

Citation: Buican, Matthew, Anatoly Dymarsky, and Rajath Radhakrishnan. "Quantum codes, CFTs, and defects." Journal of High Energy Physics 2023.3 (2023): 1-37.

Web: https://arxiv.org/abs/2112.12162

Tags: Hadamard-matrices, Conformal-field-theory, Defects/boundaries, Error-correcting-codes

This is part of a series of papers, which sketches out the relationship between quantum error correcting codes and conformal field theories in beautiful detail. In the first two articles

> Dymarsky, Anatoly, and Alfred Shapere. "Solutions of modular bootstrap constraints from quantum codes." Physical Review Letters 126.16 (2021): 161602.


> Dymarsky, Anatoly, and Alfred Shapere. "Quantum stabilizer codes, lattices, and CFTs." Journal of High Energy Physics 2021.3 (2021): 1-84.

the authors establish a way of taking in a quantum error correcting code and spitting out a conformal field theory. In the paper at hand, they study the inverse problem of what conformal field theories one can get in this process.

One fascinating feature of this theory is that it stems from a purely classical analogue: classical error correcting codes also have connections to lattices, from which one can get a lattice conformal field theory to play with. This classical analogue is due to

> Dolan, Louise, Peter Goddard, and P. Montague. "Conformal field theories, representations and lattice constructions." Communications in mathematical physics 179.1 (1996): 61-120.

Amazingly, one of the naturally occurring lattices appearing is the Leech lattice, and so the resulting conformal field theories are intimately linked to the Monster group! There is very interesting stuff to look into in this direction.