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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 ofneven-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.

 

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 chargecwe show there are code theories with the spectral gap growing linearly withc, with the coefficient saturating the conjectural upper bound. We therefore conjecture that optimal Narain theories for any value ofccan be obtained from codes.

 

Recently there has been a notable progress in the study of glueball states in lattice gauge theories, in particular extrapolating their spectrum to the limit of large number of colorsN. In this note we compare the largeNlattice results with the holographic predictions, focusing on the Klebanov-Strassler model, which describes a gauge theory with$$ \mathcal{N} $$$N$= 1 supersymmetry. We note that glueball spectrum demonstrates approximate universality across a range of gauge theory models. Because of this universality the holographic models can give reliable predictions for the spectrum of pure SU(N) Yang-Mills theories with and without supersymmetry. This is especially important for the supersymmetric theories, for which no firm lattice predictions exist yet, and the holographic models remain the most tractable approach. For SU(N) theories with largeNthe lattice non-supersymmetric and holographic supersymmetric predictions for the mass ratios of the lightest states in various sectors agree up to 5–8%, supporting the proposed universality. In particular, both lattice and holography give predictions for the 2⁺⁺and 1⁻⁻mass ratio, consistent with the known constraints on the pomeron and odderon Regge trajectories.

 

We employ semiclassical quantization to calculate spectrum of quantum KdV charges in the limit of large central chargec. Classically, KdV chargesQ_2n−1generate completely integrable dynamics on the co-adjoint orbit of the Virasoro algebra. They can be expressed in terms of action variablesI_k, e.g. as a power series expansion. Quantum-mechanically this series becomes the expansion in 1/c, while action variables become integer-valued quantum numbersn_i. Crucially, classical expression, which is homogeneous inI_k, acquires quantum corrections that include terms of subleading powers inn_k. At first two non-trivial orders in 1/cexpansion these “quantum” terms can be fixed from the analytic form ofQ_2n−1acting on the primary states. In this way we find explicit expression for the spectrum ofQ_2n−1up to first three orders in 1/cexpansion. We apply this result to study thermal expectation values ofQ_2n−1and free energy of the KdV Generalized Gibbs Ensemble.

 

We consider a UV-complete field-theoretic model in general dimensions, including d=2+1, which consists of two copies of thelong-range vector models, with O(m) and O(N-m) global symmetry groups,perturbed by double-trace operators.Using conformal perturbation theorywe find weakly-coupled IR fixed points for N\geq 6 N ≥ 6 that reveal a spontaneousbreaking of global symmetry. Namely, at finite temperature the lower rank group is broken,with the pattern persisting at all temperatures due to scale-invariance. We provide evidence that the models in question are unitary and invariant under full conformal symmetry. Furthermore, we show that this model exhibits a continuous family of weakly interacting field theories at finite N. 

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. 

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.