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Article
Physics, Particles & Fields
Johan Henriksson et al.
Summary: This paper explores the connection between two-dimensional conformal field theories defined by error-correcting codes and their generalization to quantum error-correcting codes at higher genus. It is proved that the higher-genus partition functions can be expressed as polynomials of higher-weight theta functions, and that the higher-genus modular group acts as simple linear transformations on these polynomials. The study shows that modular invariance at higher genus is more constraining than at genus 1 alone, leading to a drastic reduction in the space of possible code CFTs. The paper also discusses the application of the code polynomial form beyond the study of code CFTs.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Mathematics
Davide Gaiotto et al.
Summary: We observe that every self-dual ternary code determines a holomorphic N = 1 superconformal field theory. This provides ternary constructions of some well-known holomorphic N = 1 superconformal field theories (SCFTs), including Duncan's supermoonshine model and the fermionic beauty and the beast model of Dixon, Ginsparg, and Harvey. Along the way, we clarify some issues related to orbifolds of fermionic holomorphic CFTs. We give a simple coding-theoretic description of the supersymmetric index and conjecture that for every self-dual ternary code this index is divisible by 24; we are able to prove this conjecture except in the case when the code has length 12 mod 24. Lastly, we discuss a conjecture of Stolz and Teichner relating N = 1 SCFTs with Topological Modular Forms. This conjecture implies constraints on the supersymmetric indexes of arbitrary holomorphic SCFTs, and suggests (but does not require) that there should be, for each k, a holomorphic N = 1 SCFT of central charge 12k and index 24/ gcd( k, 24). We give ternary code constructions of SCFTs realizing this suggestion for k <= 5.
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
(2022)
Article
Physics, Particles & Fields
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)
Article
Physics, Particles & Fields
Nathan Benjamin et al.
Summary: By utilizing harmonic analysis, this article derives a crossing equation that applies only to scalar primary operators in any two-dimensional conformal field theory with U(1)(c) symmetry. The obtained crossing equation provides bounds on the scalar gap of all such theories and remarkably includes information about nontrivial zeros of the Riemann zeta function. Consequently, the Riemann hypothesis is rephrased solely as a statement regarding the asymptotic density of scalar operators in certain two-dimensional conformal field theories. Generalizations to theories with only Virasoro symmetry are also discussed.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Nikolaos Angelinos et al.
Summary: The recent connection between additive codes and Narain CFTs provides a new tool to construct theories with special properties and solve modular bootstrap constraints. Generalizing previous constructions, it is shown that all known optimal Narain theories can be constructed from codes.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Jeevan Chandra et al.
Summary: This study constrains the OPE coefficients and density of states of the 2D CFT dual to a semiclassical theory of gravity in 3D using the conformal bootstrap. By calculating in an ensemble of CFT data, it reproduces semiclassical 3D gravity. Various gravitational solutions, including wormholes and higher topology spacetimes, are analyzed and shown to agree with the ensemble-averaged CFT. The study also provides a controlled, semiclassical realization of the mechanism of Coleman, Giddings, and Strominger with random couplings induced by wormholes.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Shinichiro Yahagi
Summary: This study constructs Narain CFTs using even self-dual lattices and self-dual codes, and examines the relationship between spectral gaps and partition functions of the CFTs and the error correction capability of the codes.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Jean-Marc Schlenker et al.
Summary: In the study of AdS/CFT correspondence, the puzzle of amplitudes associated with connected bulk manifolds and disconnected boundaries has been a longstanding mystery. This paper sharpens the puzzle by analyzing a class of observables that do not show effects of ensemble averaging. These observables involve states that are above the ground state by a fixed amount in the large N limit, and are far from being black hole states. The authors explore the example of D=3 and prove that connected solutions of Einstein's equations with disconnected boundaries do not contribute to these observables. The apparent ensemble averaging in some observables is proposed to be a reflection of the chaotic nature of black hole physics and the absence of a large N limit in the Hilbert space describing black holes.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Scott Collier et al.
Summary: We propose a new approach to extract the physical consequences of S-duality of four-dimensional N = 4 super Yang-Mills (SYM) and its string theory dual using SL(2, Z) spectral theory. Our method can constrain the analytic structure of N = 4 SYM data and has implications for the structure of instantons. In large N limits, we derive the existence and scaling of non-perturbative effects. We also discuss the implications for holography and embedding ensemble averaging into the traditional AdS/CFT paradigm.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
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)
Article
Physics, Particles & Fields
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)
Article
Physics, Particles & Fields
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)
Article
Physics, Multidisciplinary
Anatoly Dymarsky et al.
Summary: Modular invariance imposes strict constraints on the partition functions of CFTs, leading to fundamental results. This study establishes a connection between a family of quantum error correcting codes and code CFI's, simplifying the modular invariance of 2D CFT partition functions.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Particles & Fields
Jordan Cotler et al.
Summary: In this study, we computed the path integral of three-dimensional gravity on spaces with a torus times an interval topology, revealing spectral correlations between BTZ black hole microstates near threshold and the spectral form factor at fixed momentum. Our findings indicate that the low-energy limit of these correlations aligns precisely with a double-scaled random matrix ensemble with Virasoro symmetry.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Nathan Benjamin et al.
Summary: The text discusses the application of harmonic analysis theory to study the partition functions of two-dimensional conformal field theories, decomposing them into eigenfunctions of different moduli spaces and exploring their relevance to AdS(3) gravity. It emphasizes that the local operator spectrum is fully determined by a specific subset of degeneracies.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
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Jeffrey A. Harvey et al.
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(2020)
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Thomas Hartman et al.
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(2019)
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Ethan Dyer et al.
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(2018)
Correction
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Jordan S. Cotler et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2018)
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Scott Collier et al.
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(2018)
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Physics, Particles & Fields
Christoph A. Keller et al.
ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS
(2018)
Article
Mathematics
Henry Cohn et al.
ANNALS OF MATHEMATICS
(2017)
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Maryna S. Viazovska
ANNALS OF MATHEMATICS
(2017)
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Christoph A. Keller et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2015)
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Matthias R. Gaberdiel et al.
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(2014)
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Hai Siong Tan
JOURNAL OF HIGH ENERGY PHYSICS
(2014)
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Matthias R. Gaberdiel et al.
Communications in Number Theory and Physics
(2013)
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Jan Manschot et al.
Communications in Number Theory and Physics
(2013)
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Stefka Bouyuklieva et al.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2012)
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Alejandra Castro et al.
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JOURNAL OF HIGH ENERGY PHYSICS
(2010)
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A. McIntyre et al.
GEOMETRIC AND FUNCTIONAL ANALYSIS
(2006)
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EM Rains
IEEE TRANSACTIONS ON INFORMATION THEORY
(2003)
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RT Bilous et al.
DESIGNS CODES AND CRYPTOGRAPHY
(2002)
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I Krasikov et al.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2000)
