Narain CFTs and error-correcting codes on finite fields

Article Physics, Particles & Fields

Classical codes and chiral CFTs at higher genus

Johan Henriksson et al.

Summary: This paper investigates the higher genus modular invariance of two-dimensional conformal field theories (CFTs). It derives explicit expressions for the higher genus partition functions of a specific class of CFTs called code CFTs, which are constructed using classical error-correcting codes. The study finds that the constraints from higher genus modular invariance and consistency under degeneration limits greatly reduce the number of possible code CFTs. This work provides an important step towards understanding the constraints from higher genus modular invariance on 2D CFTs.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

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Article Physics, Particles & Fields

Free partition functions and an averaged holographic duality

Nima Afkhami-Jeddi et al.

Summary: The study focuses on the torus partition functions of free bosonic CFTs in two dimensions, showing that integrating over Narain moduli defines an ensemble-averaged free CFT and the averaged partition function can be reinterpreted as a sum over topologies in three dimensions. This leads to the conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)(c)xU(1)(c) symmetry and a composite boundary graviton. Additionally, general constraints on the spectral gap of free CFTs are obtained for small central charge c, Narain compactifications with a large gap are constructed, and an analytic bootstrap functional corresponding to a single self-dual boson is found using the spinning modular bootstrap.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

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Article Physics, Particles & Fields

Non-rational Narain CFTs from codes over F4

Anatoly Dymarsky et al.

Summary: The study establishes a mapping between a class of codes over F-4 and a family of nonrational Narain CFTs, complementing a recent relation between quantum stabilizer codes and rational Narain theories. A polynomial ansatz for the partition function is formulated from the modular bootstrap perspective, simplifying modular invariance to a few algebraic constraints that are easy to solve. The construction yields optimal theories for certain small values of central charge, maximizing the spectral gap value.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

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Article Physics, Particles & Fields

Comments on the holographic description of Narain theories

Anatoly Dymarskya et al.

Summary: This study discusses the holographic description of Narain U(1)(c) x U(1)(c) conformal field theories, proposing a hypothesis that the density of states of any Narain theory in the large central charge limit is bounded by the density of states of U(1) gravity. Testing this proposal using chiral lattice CFTs and CFTs based on quantum stabilizer codes reveals new bounds on quantum stabilizer codes and the exponentially small density variance in the central charge limit.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

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Review Quantum Science & Technology

Holographic tensor network models and quantum error correction: a topical review

Alexander Jahn et al.

Summary: Recent progress in holographic dualities, combining insights from string theory with concepts from quantum information theory, has led to successful approaches involving tensor networks. These approaches capture holographic properties, meaningful correlations of holographic boundary states, and features of quantum error correction in holography. This topical review provides an overview of recent successful realizations of such models by introducing theoretical foundations of AdS/CFT and necessary quantum information concepts.

QUANTUM SCIENCE AND TECHNOLOGY (2021)

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Article Physics, Particles & Fields