Analytic bootstrap of mixed correlators in the \(O(n)\) CFT. (English) Zbl 1534.81084
Summary: We use large spin perturbation theory and the Lorentzian inversion formula to compute order-\(\epsilon\) corrections to mixed correlators in the \(O(n)\) Wilson-Fisher CFT in \(4 - \epsilon\) dimensions. In particular, we find the scaling dimensions and averaged OPE coefficients appearing in all correlators involving the operators \(\varphi\) and \(\varphi^2\), for \(\varphi^2\) in both the singlet and symmetric traceless representations of \(O(n)\). We extend some computations to the next order, and find order-\(\epsilon^2\) data for a number of quantities for the Ising case at \(n = 1\). Along the way, we discuss several interesting technical aspects which arise, including subleading corrections to mixed conformal blocks, projections onto higher twists in the inversion formula, and multiplet recombination.
MSC:
| 81T11 | Higher spin theories |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
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