On critical exponents without Feynman diagrams

Abstract

In order to achieve a better analytic handle on the modern conformal bootstrap program, we re-examine and extend the pioneering 1974 work of Polyakov's, which was based on consistency between the operator product expansion and unitarity. As in the bootstrap approach, this method does not depend on evaluating Feynman diagrams. We show how this approach can be used to compute the anomalous dimensions of certain operators in the $O(n)$ model at the Wilson-Fisher fixed point in $4-\epsilon$ dimensions up to $O({\epsilon }^2)$.

27 pages, 1 figure, Comments added. Typos corrected

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• Eikonalization of Conformal Blocks
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• Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
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• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
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• On the Polyakov-Mellin bootstrap
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• Conformal correlators as simplex integrals in momentum space
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• Anomalous Dimensions from Crossing Kernels
• Dispersion relations and exact bounds on CFT correlators
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• $\epsilon$-Expansion in the Gross-Neveu Model from Conformal Field Theory
• Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect
• Positivity and Geometric Function Theory Constraints on Pion Scattering
• Revisiting the dilatation operator of the Wilson-Fisher fixed point
• Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT
• Inverse Bootstrapping Conformal Field Theories
• The $\epsilon$-expansion of the codimension two twist defect from conformal field theory
• Crossing antisymmetric Polyakov blocks + Dispersion relation
• Renormalization and non-renormalization of scalar EFTs at higher orders
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• Charging Up the Functional Bootstrap
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• From conformal correlators to analytic S-matrices: CFT${}_1$/QFT${}_2$
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• Aspects of Higher Spin Theories, Conformal Field Theories and Holography
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• Bootstrap Method in Theoretical Physics