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arXiv · 2205.09132

Analytic bootstrap of mixed correlators in the $\boldsymbol{O(n)}$ CFT

Francesco Bertucci·Johan Henriksson·Brian McPeak
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Abstract

We use large spin perturbation theory and the Lorentzian inversion formula to compute order-$\varepsilon$ corrections to mixed correlators in the $O(n)$ Wilson-Fisher CFT in $4 - \varepsilon$ dimensions. In particular, we find the scaling dimensions and averaged OPE coefficients appearing in all correlators involving $\varphi$ 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-$\varepsilon^2$ 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.

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Francesco Bertucci, Johan Henriksson, Brian McPeak. 2022-05-18. Analytic bootstrap of mixed correlators in the $\boldsymbol{O(n)}$ CFT. https://arxiv.org/abs/2205.09132

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