Boundary and Interface CFTs from the Conformal Bootstrap

Abstract

We explore some consequences of the crossing symmetry for defect conformal field theories, focusing on codimension one defects like flat boundaries or interfaces. We study surface transitions of the 3d Ising and other O(N) models through numerical solutions to the crossing equations with the method of determinants. In the extraordinary transition, where the low-lying spectrum of the surface operators is known, we use the bootstrap equations to obtain information on the bulk spectrum of the theory. In the ordinary transition the knowledge of the low-lying bulk spectrum allows to calculate the scale dimension of the relevant surface operator, which compares well with known results of two-loop calculations in 3d. Estimates of various OPE coefficients are also obtained. We also analyze in 4-epsilon dimensions the renormalization group interface between the O(N) model and the free theory and check numerically the results in 3d.

40 pages, many figures v2: new results on 3d O(N) bulk spectrum added, one appendix eliminated, typos corrected, references updated. v3: two references to high precision Monte Carlo data added; they nicely agree with our bootstrap calculations. Matches published version. v4: results for the extraordinary transition for N=2,3 removed: see added note

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• Bootstrapping Mixed Correlators in the 3D Ising Model
• Bounds on 4D Conformal and Superconformal Field Theories
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap
• Defects and Bulk Perturbations of Boundary Landau-Ginzburg Orbifolds
• The thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class
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Cited by in corpus (119)

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• A General Proof of the Quantum Null Energy Condition
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• Recursion Relations for Conformal Blocks
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• Renormalization Group Flows on Line Defects
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• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
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• On Higher-dimensional Carrollian and Galilean Conformal Field Theories
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• Bootstrapping the 3d Ising model at finite temperature
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