An Algebraic Approach to the Analytic Bootstrap
TLDR
In this article, an algebraic approach to the analytic bootstrap in CFTs is presented, which maps the problem of doing large spin sums to any desired order to the problem solving a set of recursion relations.Abstract:
We develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired order to the problem of solving a set of recursion relations. We compute corrections to the anomalous dimension of large spin operators due to the exchange of a primary and its descendants in the crossed channel and show that this leads to a Borel-summable expansion. We analyse higher order corrections to the microscopic CFT data in the direct channel and its matching to infinite towers of operators in the crossed channel. We apply this method to the critical O(N ) model. At large N we reproduce the first few terms in the large spin expansion of the known two-loop anomalous dimensions of higher spin currents in the traceless symmetric representation of O(N ) and make further predictions. At small N we present the results for the truncated large spin expansion series of anomalous dimensions of higher spin currents.read more
Citations
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Journal ArticleDOI
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
TL;DR: Conformal field theories have been long known to describe the universal physics of scale invariant critical points as discussed by the authors, and they describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same time sit at the heart of our modern understanding of quantum field theory.
Book
EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions
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Light-ray operators in conformal field theory
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The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
TL;DR: In this paper, the dimensions and OPE coefficients of several operators in the 3D Ising CFT were computed numerically, and then the solution to crossing symmetry was reverse-engineered analytically.
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A spacetime derivation of the Lorentzian OPE inversion formula
TL;DR: In this paper, Cararon-Huot et al. give a new derivation of this formula based on Wick rotation in spacetime rather than cross-ratio space, which sheds light on previous observations about the chaos regime in the SYK model.
References
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Andrea Pelissetto,Ettore Vicari +1 more
TL;DR: In this paper, the critical behavior of spin systems at equilibrium is studied in three and two dimensions, and the results in three-dimensional space are presented in particular for the six-loop perturbative series for the β -functions.
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Solving the 3D Ising Model with the Conformal Bootstrap
Sheer El-Showk,Miguel F. Paulos,David Poland,Slava Rychkov,David Simmons-Duffin,Alessandro Vichi +5 more
TL;DR: In this article, the constraints of crossing symmetry and unitarity in general 3D conformal field theories were studied, and it was shown that the 3D Ising model lies at a corner point on the boundary of the allowed parameter space.
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Conformal four point functions and the operator product expansion
F.A. Dolan,Hugh Osborn +1 more
TL;DR: In this paper, a recurrence relation for the function corresponding to the contribution of an arbitrary spin field in the operator product expansion to the four point function for scalar fields in conformally invariant theories is derived.
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The analytic bootstrap and AdS superhorizon locality
TL;DR: In this article, it was shown that every CFT with a scalar operator ϕ must contain infinite sequences of operators with twist approaching τ → 2Δ + 2n for each integer n as l → ∞.