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Register a new userCritical O(N) model to order $epsilon^4$ from analytic bootstrap
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We compute, using the method of large spin perturbation theory, the anomalous dimensions and OPE coefficients of all leading twist operators in the critical $ O(N) $ model, to fourth order in the $ epsilon $-expansion. This is done fully within a bootstrap framework, and generalizes a recent result for the CFT-data of the Wilson-Fisher model. The anomalous dimensions we obtain for the $ O(N) $ singlet operators agree with the literature values, obtained by diagrammatic techniques, while the anomalous dimensions for operators in other representations, as well as all OPE coefficients, are new. From the results for the OPE coefficients, we derive the $ epsilon^4 $ corrections to the central charges $ C_T $ and $ C_J $, which are found to be compatible with the known large $ N $ expansions. Predictions for the central charge in the strongly coupled 3d model, including the 3d Ising model, are made for various values of $ N $, which compare favourably with numerical results and previous predictions.
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In this work, a second-order transport coefficient (the curvature-matter coupling $kappa$) is calculated exactly for the 3+1d O(N) model at large N for any coupling value. Since the theory is `trivial in the sense of possessing a Landau pole, the result for $kappa$ only is free from cut-off artifacts much below the Landau pole in the effective field theory sense. Nevertheless, this leaves a large range of coupling values where this transport coefficient can be determined non-perturbatively and analytically with little ambiguity. Along with thermodyamic results also calculated in this work, I expect exact large N results to provide good quantitative predictions for N=1 scalar field theory with $phi^4$ interaction.
Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with $O(m)times O(n)$ global symmetry in $d=3$ spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in $varepsilon=4-d$ and in $1/n$, with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for $O(2)times O(n)$ theories for various values of $n$. Some of these islands can be attributed to fixed points predicted by perturbative methods like the $varepsilon$ and large-$n$ expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.
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