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Register a new userAnomalous dimensions at large charge in d=4 O(N) theory
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Recently it was shown that the scaling dimension of the operator $phi^n$ in $lambda(phi^*phi)^2$ theory may be computed semi-classically at the Wilson-Fisher fixed point in $d=4-epsilon$, for generic values of $lambda n$ and this was verified to two loop order in perturbation theory at leading and sub-leading $n$. In subsequent work, this result was generalised to operators of fixed charge $Q$ in $O(N)$ theory and verified up to three loops in perturbation theory at leading and sub-leading order. Here we extend this verification to four loops in $O(N)$ theory, once again at leading and sub-leading order. We also investigate the strong-coupling regime.
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We compute four-point correlation functions of scalar composite operators in the N=4 supercurrent multiplet at order g^4 using the N=1 superfield formalism. We confirm the interpretation of short-distance logarithmic behaviours in terms of anomalous dimensions of unprotected operators exchanged in the intermediate channels and we determine the two-loop contribution to the anomalous dimension of the N=4 Konishi supermultiplet.
Recently it was shown that the scaling dimension of the operator $phi^n$ in $lambda(barphiphi)^2$ theory may be computed semiclassically at the Wilson-Fisher fixed point in $d=4-epsilon$, for generic values of $lambda n$, and this was verified to two loop order in perturbation theory at leading and subleading $n$. This result was subsequently generalised to operators of fixed charge $Q$ in $O(N)$ theory and verified up to four loops in perturbation theory at leading and subleading $Q$. More recently, similar semiclassical calculations have been performed for the classically scale-invariant $U(N)times U(N)$ theory in four dimensions, and verified up to two loops, once again at leading and subleading $Q$. Here we extend this verification to four loops. We also consider the corresponding classically scale-invariant theory in three dimensions, similarly verifying the leading and subleading semiclassical results up to four loops in perturbation theory.
In a {cal N}=1 superspace formulation of {cal N}=4 Yang-Mills theory we obtain the anomalous dimensions of chiral operators with large R charge J to infty keeping g^2 N/J^2 finite, to all orders of perturbation theory in the planar limit. Our result proves the conjecture that the anomalous dimensions are indeed finite in the above limit. This amounts to an exact check of the proposed duality between a sector of {cal N}=4 Yang-Mills theory with large R charge J and string theory in a pp-wave background.
Recently it was shown that the scaling dimension of the operator $phi^n$ in scale-invariant $d=3$ theory may be computed semiclassically, and this was verified to leading order (two loops) in perturbation theory at leading and subleading $n$. Here we extend this verification to six loops, once again at leading and subleading $n$. We then perform a similar exercise for a theory with a multiplet of real scalars and an $O(N)$ invariant hexic interaction. We also investigate the strong-coupling regime for this example.
We present numerical results for the nonplanar lightlike cusp and collinear anomalous dimension at four loops in ${mathcal N} = 4$ SYM theory, which we infer from a calculation of the Sudakov form factor. The latter is expressed as a rational linear combination of uniformly transcendental integrals for arbitrary colour factor. Numerical integration in the nonplanar sector reveals explicitly the breakdown of quadratic Casimir scaling at the four-loop order. A thorough analysis of the reported numerical uncertainties is carried out.
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