ε-Expansions Near Three Dimensions from Conformal Field Theory
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We formally extend the CFT techniques introduced in arXiv:1505.00963, to $\phi^{\frac{2d_0}{d_0-2}}$ theory in $d=d_0-\epsilon$ dimensions and use it to compute anomalous dimensions near $d_0=3, 4$ in a unified manner. We also do a similar analysis of the $O(N)$ model in three dimensions by developing a recursive combinatorial approach for OPE contractions. Our results match precisely with low loop perturbative computations. Finally, using 3-point correlators in the CFT, we comment on why the $\phi^3$ theory in $d_0=6$ is qualitatively different.
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Cited by 2 Pith papers
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$\phi^6$ at $6$ (and some $8$) loops in $3d$
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