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17 papers found.
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The lightcone bootstrap and the spectrum of the 3d Ising CFT

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 for computing infinite sums of SL(2, \( \mathrm{\mathbb{R}} \)) conformal blocks. Using these techniques, we solve the lightcone bootstrap to all orders in an...

Bootstrapping 3D fermions with global symmetries

We study the conformal bootstrap for 4-point functions of fermions 〈ψ i ψ j ψ k ψ ℓ 〉 in parity-preserving 3d CFTs, where ψ i transforms as a vector under an O(N ) global symmetry. We compute bounds on scaling dimensions and central charges, finding features in our bounds that appear to coincide with the O(N ) symmetric Gross-Neveu-Yukawa fixed points. Our computations are in...

Looking for a bulk point

We consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space Landau diagram with null lines. In theories with gravity duals, we can also draw Landau diagrams in the bulk. We argue that certain singularities can arise only from bulk diagrams, not from boundary diagrams. As has been previously observed, these...

A semidefinite program solver for the conformal bootstrap

We introduce SDPB: an open-source, parallelized, arbitrary-precision semidefinite program solver, designed for the conformal bootstrap. SDPB significantly outperforms less specialized solvers and should enable many new computations. As an example application, we compute a new rigorous high-precision bound on operator dimensions in the 3d Ising CFT, Δ σ = 0.518151(6), Δ ϵ = 1...

\( \mathcal{N} \) = 4 superconformal bootstrap of the K3 CFT

We study two-dimensional (4, 4) superconformal field theories of central charge c = 6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap. This is made possible through a surprising relation between the BPS \( \mathcal{N} \) = 4 superconformal blocks with c = 6 and bosonic Virasoro conformal blocks with c = 28, and an exact result on the...

Precision islands in the Ising and O(N ) models

We make precise determinations of the leading scaling dimensions and operator product expansion (OPE) coefficients in the 3d Ising, O(2), and O(3) models from the conformal bootstrap with mixed correlators. We improve on previous studies by scanning over possible relative values of the leading OPE coefficients, which incorporates the physical information that there is only a...

Projectors, shadows, and conformal blocks

David Simmons-Duffin 0 Open Access 0 c The Authors. Article funded by SCOAP 0 0 Jefferson Physical Laboratory, Harvard University , Cambridge, MA 02138 U.S.A We introduce a method for computing

Bootstrapping the O(N) archipelago

We study 3d CFTs with an O(N) global symmetry using the conformal bootstrap for a system of mixed correlators. Specifically, we consider all nonvanishing scalar four-point functions containing the lowest dimension O(N) vector ϕ i and the lowest dimension O(N) singlet s, assumed to be the only relevant operators in their symmetry representations. The constraints of crossing...

Bootstrapping mixed correlators in the 3D Ising model

We study the conformal bootstrap for systems of correlators involving nonidentical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We apply this formalism to the simplest system of mixed correlators in 3D CFTs with a ℤ2 global symmetry. For the leading ℤ2-odd operator σ and ℤ2...

Fermion-scalar conformal blocks

We compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called ‘seed blocks’ in three dimensions. Conformal blocks associated with 4-point functions of operators with arbitrary spins can now be determined from these seed blocks...

Bootstrapping 3D fermions

We study the conformal bootstrap for a 4-point function of fermions 〈ψψψψ〉 in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ × ψ OPE, and also on the central charge C T . We observe features in our...

Bootstrapping the O(N ) vector models

We study the conformal bootstrap for 3D CFTs with O(N ) global symmetry. We obtain rigorous upper bounds on the scaling dimensions of the first O(N ) singlet and symmetric tensor operators appearing in the ϕ i × ϕ j OPE, where ϕ i is a fundamental of O(N ). Comparing these bounds to previous determinations of critical exponents in the O(N ) vector models, we find strong numerical...

\( \mathcal{N} \) = 1 superconformal blocks for general scalar operators

We use supershadow methods to derive new expressions for superconformal blocks in 4d \( \mathcal{N} \) = 1 superconformal field theories. We analyze the four-point function \( \left\langle {\mathcal{A}}_1{\mathcal{A}}_2^{\dagger }{\mathrm{\mathcal{B}}}_1{\mathrm{\mathcal{B}}}_2^{\dagger}\right\rangle \), where \( \mathcal{A} \) i and ℬ i are scalar superconformal primary...

Covariant approaches to superconformal blocks

We develop techniques for computing superconformal blocks in 4d superconformal field theories. First we study the super-Casimir differential equation, deriving simple new expressions for superconformal blocks for 4-point functions containing chiral operators in theories with \( \mathcal{N} \)-extended supersymmetry. We also reproduce these results by extending the “shadow...