Abstract
We study large charge sectors in the O(N) model in 6 − ϵ dimensions. For 4 < d < 6, in perturbation theory, the quartic O(N) theory has a UV stable fixed point at large N . It was recently argued that this fixed point can be described in terms of an IR fixed point of a cubic O(N) model. By considering a double scaling limit of large charge and weak couplings, we compute two-point and all “extremal” higher-point correlation functions for large charge operators and find a precise equivalence between both pictures. Instanton instabilities are found to be exponentially suppressed at large charge. We also consider correlation function of U(1)-invariant meson operators in the O(2N) ⊃ U(1) × SU(N) theory, as a first step towards tests of (higher spin) AdS/CFT.
Highlights
The upper critical dimension of the quartic interaction is 4
We study large charge sectors in the O(N ) model in 6 − dimensions
The quartic model is most conveniently studied upon performing a Hubbard-Stratonovich (HS) transformation [10, 25], which effectively converts it into a cubic model albeit with no dynamics for the HS scalar field
Summary
In the theory (2.1), the elementary fields φi fill a vector representation of O(2N ), whose Dynkin labels are [1, 0, · · · , 0]DN. These equations reproduce the ones obtained for the leading order in the perturbation series, which, with the current scaling, become exact. This is the precise analog of the limit considered in [40, 46], with the difference that there is an additional field η, which mediates the interaction. Just as for the cubic theory, the diagram on the left panel is suppressed with respect to the diagram on the right panel of figure 4 in the large n limit by a factor 1/n. This precisely recovers the second line in (2.38) (evaluated at the fixed point), implying a striking match with the anomalous dimension computed from the cubic theory
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