A bstract There is a rich connection between classical errorcorrecting codes, Euclidean lattices, and chiral conformal field theories. Here we show that quantum errorcorrecting codes, those of the stabilizer type, are related to Lorentzian lattices and nonchiral CFTs. More specifically, real selfdual stabilizer codes can be associated with even selfdual Lorentzian lattices, and thus define Narain CFTs. We dub the resulting theories code CFTs and study their properties. Tduality transformations of a code CFT, at the level of the underlying code, reduce to code equivalences. By means of such equivalences, any stabilizer code can be reduced to a graph code. We can therefore represent code CFTs by graphs. We study code CFTs with small central charge c = n ≤ 12, and find many interesting examples. Among them is a nonchiral E 8 theory, which is based on the root lattice of E 8 understood as an even selfdual Lorentzian lattice. By analyzing all graphs with n ≤ 8 nodes we find many pairs and triples of physically distinct isospectral theories. We also construct numerous modular invariant functions satisfying all the basic properties expected of the CFT partition function, yet which are not partition functions of any known CFTs. Wemore »
Comments on the holographic description of Narain theories
A bstract We discuss the holographic description of Narain U(1) c × U(1) c conformal field theories, and their potential similarity to conventional weakly coupled gravitational theories in the bulk, in the sense that the effective IR bulk description includes “U(1) gravity” amended with additional light degrees of freedom. Starting from this picture, we formulate the hypothesis that in the large central charge limit the density of states of any Narain theory is bounded by below by the density of states of U(1) gravity. This immediately implies that the maximal value of the spectral gap for primary fields is ∆ 1 = c /(2 πe ). To test the selfconsistency of this proposal, we study its implications using chiral lattice CFTs and CFTs based on quantum stabilizer codes. First we notice that the conjecture yields a new bound on quantum stabilizer codes, which is compatible with previously known bounds in the literature. We proceed to discuss the variance of the density of states, which for consistency must be vanishingly small in the large c limit. We consider ensembles of code and chiral theories and show that in both cases the density variance is exponentially small in the central charge.
 Award ID(s):
 2013812
 Publication Date:
 NSFPAR ID:
 10348656
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2021
 Issue:
 10
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
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