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 self-consistency 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.
more »
« less
Optimal Narain CFTs from codes
Recently established connection between additive codes and Narain CFTs provides a new tool to construct theories with special properties and solve modular bootstrap constraints by reducing them to algebraic identities. We generalize previous constructions to include many new theories, in particular we show that all known optimal Narain theories, i.e. those maximizing the value of spectral gap, can be constructed from codes. For asymptotically large central charge
- Award ID(s):
- 2013812
- NSF-PAR ID:
- 10483047
- Publisher / Repository:
- Springer (Journal of High Energy Physics)
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2022
- Issue:
- 11
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
A bstract We construct a map between a class of codes over F 4 and a family of non-rational Narain CFTs. This construction is complementary to a recently introduced relation between quantum stabilizer codes and a class of rational Narain theories. From the modular bootstrap point of view we formulate a polynomial ansatz for the partition function which reduces modular invariance to a handful of algebraic easy-to-solve constraints. For certain small values of central charge our construction yields optimal theories, i.e. those with the largest value of the spectral gap.more » « less
-
more » « less
A<sc>bstract</sc> We give a general construction relating Narain rational conformal field theories (RCFTs) and associated 3d Chern-Simons (CS) theories to quantum stabilizer codes. Starting from an abelian CS theory with a fusion group consisting of
n even-order factors, we map a boundary RCFT to ann -qubit quantum code. When the relevant ’t Hooft anomalies vanish, we can orbifold our RCFTs and describe this gauging at the level of the code. Along the way, we give CFT interpretations of the code subspace and the Hilbert space of qubits while mapping error operations to CFT defect fields. -
null (Ed.)A bstract There is a rich connection between classical error-correcting codes, Euclidean lattices, and chiral conformal field theories. Here we show that quantum error-correcting codes, those of the stabilizer type, are related to Lorentzian lattices and non-chiral CFTs. More specifically, real self-dual stabilizer codes can be associated with even self-dual Lorentzian lattices, and thus define Narain CFTs. We dub the resulting theories code CFTs and study their properties. T-duality 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 non-chiral E 8 theory, which is based on the root lattice of E 8 understood as an even self-dual 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. We consider the ensemble average over all code theories, calculate the corresponding partition function, and discuss its possible holographic interpretation. The paper is written in a self-contained manner, and includes an extensive pedagogical introduction and many explicit examples.more » « less
-
more » « less
Abstract We take a broad look at the problem of identifying the magnetic solar causes of space weather. With the lackluster performance of extrapolations based upon magnetic field measurements in the photosphere, we identify a region in the near-UV (NUV) part of the spectrum as optimal for studying the development of magnetic free energy over active regions. Using data from SORCE, the Hubble Space Telescope, and SKYLAB, along with 1D computations of the NUV spectrum and numerical experiments based on the MURaM radiation–magnetohydrodynamic and HanleRT radiative transfer codes, we address multiple challenges. These challenges are best met through a combination of NUV lines of bright Mg
ii , and lines of Feii and Fei (mostly within the 4s –4p transition array) which form in the chromosphere up to 2 × 104K. Both Hanle and Zeeman effects can in principle be used to derive vector magnetic fields. However, for any given spectral line theτ = 1 surfaces are generally geometrically corrugated owing to fine structure such as fibrils and spicules. By using multiple spectral lines spanning different optical depths, magnetic fields across nearly horizontal surfaces can be inferred in regions of low plasmaβ , from which free energies, magnetic topology, and other quantities can be derived. Based upon the recently reported successful sub-orbital space measurements of magnetic fields with the CLASP2 instrument, we argue that a modest space-borne telescope will be able to make significant advances in the attempts to predict solar eruptions. Difficulties associated with blended lines are shown to be minor in an Appendix.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP11(2022)118
