Conformal field theory
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The conformal bootstrap: Theory, numerical techniques, and applications Open
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same …
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Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality Open
In this Letter we prove a simple theorem in quantum information theory, which implies that bulk operators in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence can be reconstructed as CFT operators in a spatial subregion A,…
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Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory Open
We study chaotic dynamics in two-dimensional conformal field theory through out-of-time-order thermal correlators of the form ⟨W(t)VW(t)V⟩. We reproduce holographic calculations similar to those of Shenker and Stanford, by studying the lar…
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Quantum quenches in 1 + 1 dimensional conformal field theories Open
We review the imaginary time path integral approach to the quench dynamics of conformal field theories. We show how this technique can be applied to the determination of the time dependence of correlation functions and entanglement entropy…
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Virasoro conformal blocks and thermality from classical background fields Open
We show that in 2d CFTs at large central charge, the coupling of the stress\ntensor to heavy operators can be re-absorbed by placing the CFT in a\nnon-trivial background metric. This leads to a more precise computation of the\nVirasoro con…
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Higher spin realization of the DS/CFT correspondence Open
We conjecture that Vasiliev's theory of higher spin gravity in four-dimensional de Sitter space (dS4) is holographically dual to a three-dimensional conformal field theory (CFT3) living on the spacelike boundary of dS4 at future timelike i…
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Entanglement entropy: Holography and renormalization group Open
Entanglement entropy plays a variety of roles in quantum field theory, including the connections between quantum states and gravitation through the holographic principle. This article provides a review of entanglement entropy from a mixed …
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Anti–de Sitter Space from Optimization of Path Integrals in Conformal Field Theories Open
We introduce a new optimization procedure for Euclidean path integrals, which compute wave functionals in conformal field theories (CFTs). We optimize the background metric in the space on which the path integration is performed. Equivalen…
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Large Spin Perturbation Theory for Conformal Field Theories Open
We consider conformal field theories around points of large twist degeneracy. Examples of this are theories with weakly broken higher spin symmetry and perturbations around generalized free fields. At the degenerate point we introduce twis…
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Quantum Hall physics: Hierarchies and conformal field theory techniques Open
The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past 30 years, has generated many ground-breaking new ideas and concepts. Very early on it was realized that the zoo of emer…
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Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases Open
Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limite…
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Light-ray operators in conformal field theory Open
We argue that every CFT contains light-ray operators labeled by a continuous spin J. When J is a positive integer, light-ray operators become integrals of local operators over a null line. However for non-integer J , light-ray operators ar…
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Conformal field theory out of equilibrium: a review Open
We provide a pedagogical review of the main ideas and results in non-equilibrium conformal field theory and connected subjects. These concern the understanding of quantum transport and its statistics at and near critical points. Starting w…
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Integral geometry and holography Open
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is define…
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Topological defects on the lattice: I. The Ising model Open
In this paper and its sequel, we construct topologically invariant defects in\ntwo-dimensional classical lattice models and quantum spin chains. We show how\ndefect lines commute with the transfer matrix/Hamiltonian when they obey the\ndef…
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Unitarity and the Holographic S-Matrix Open
The bulk S-Matrix can be given a non-perturbative definition in terms of the flat space limit of AdS/CFT. We show that the unitarity of the S-Matrix, ie the optical theorem, can be derived by studying the behavior of the OPE and the confor…
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Out-of-time-ordered correlators in a quantum Ising chain Open
Out-of-time-ordered correlators (OTOC) have been proposed to characterize quantum chaos in generic systems. However, they can also show interesting behavior in integrable models, resembling the OTOC in chaotic systems in some aspects. Here…
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Entanglement Entropy in Galilean Conformal Field Theories and Flat Holography Open
We present the analytical calculation of entanglement entropy for a class of two-dimensional field theories governed by the symmetries of the Galilean conformal algebra, thus providing a rare example of such an exact computation. These fie…
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An integrable Lorentz-breaking deformation of two-dimensional CFTs Open
It has been recently shown that the deformation of an arbitrary two-dimensional conformal field theory by the composite irrelevant operator T \bar T , built from the components of the stress tensor, is solvable; in particular, the fi…
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Emergent SO(5) Symmetry at the Néel to Valence-Bond-Solid Transition Open
We show numerically that the "deconfined" quantum critical point between the Néel antiferromagnet and the columnar valence-bond solid, for a square lattice of spin 1/2, has an emergent SO(5) symmetry. This symmetry allows the Néel vector a…
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Universality of Corner Entanglement in Conformal Field Theories Open
We study the contribution to the entanglement entropy of (2+1)-dimensional conformal field theories (CFTs) coming from a sharp corner in the entangling surface. This contribution is encoded in a function a(θ) of the corner opening angle, a…
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Conformal Bootstrap in Mellin Space Open
We propose a new approach towards analytically solving for the dynamical content of conformal field theories (CFTs) using the bootstrap philosophy. This combines the original bootstrap idea of Polyakov with the modern technology of the Mel…
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TASI Lectures on the Emergence of Bulk Physics in AdS/CFT Open
These lectures review recent developments in our understanding of the emergence of local bulk physics in AdS/CFT. The primary topics are sufficient conditions for a conformal field theory to have a semiclassical dual, bulk reconstruction, …
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Entanglement Wedge Cross Section from the Dual Density Matrix Open
We define a new information theoretic quantity called odd entanglement entropy (OEE) which enables us to compute the entanglement wedge cross section in holographic conformal field theories (CFTs). The entanglement wedge cross section has …
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Correlation functions of Coulomb branch operators Open
We consider the correlation functions of Coulomb branch operators in four-dimensional N=2 Superconformal Field Theories (SCFTs) involving exactly one anti-chiral operator. These extremal correlators are the "minimal" non-holomorphic local …
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Entwinement and the emergence of spacetime Open
It is conventional to study the entanglement between spatial regions of a quantum field theory. However, in some systems entanglement can be dominated by “internal”, possibly gauged, degrees of freedom that are not spatially organized, and…
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Bi-local holography in the SYK model: perturbations Open
We continue the study of the Sachdev-Ye-Kitaev model in the Large N limit. Following our formulation in terms of bi-local collective fields with dynamical reparametrization symmetry, we perform perturbative calculations around the conforma…
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Entanglement spectrum and entropy in topological non-Hermitian systems and nonunitary conformal field theory Open
We propose a method of computing and studying entanglement quantities in\nnon-Hermitian systems by use of a biorthogonal basis. We find that the\nentanglement spectrum characterizes the topological properties in terms of the\nexistence of …
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The lightcone bootstrap and the spectrum of the 3d Ising CFT Open
In this paper. we compute numerically the dimensions and OPE coefficients of several operators in the 3d Ising CFT, and then try to reverse-engineer the solution to crossing symmetry analytically. Our key tool is a set of new techniques fo…
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Conformal invariance and quantum nonlocality in critical hybrid circuits Open
We establish the emergence of a conformal field theory (CFT) in a (1+1)-dimensional hybrid quantum circuit right at the measurement-driven entanglement transition by revealing space-time conformal covariance of entanglement entropies and m…