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Register a new userCorrelation functions in scalar field theory at large charge
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We compute general higher-point functions in the sector of large charge operators $phi^n$, $barphi^n$ at large charge in $O(2)$ $(bar phiphi)^2$ theory. We find that there is a special class of extremal correlators having only one insertion of $bar phi^n$ that have a remarkably simple form in the double-scaling limit $nto infty $ at fixed $g,n^2equiv lambda$, where $gsimepsilon $ is the coupling at the $O(2)$ Wilson-Fisher fixed point in $4-epsilon$ dimensions. In this limit, also non-extremal correlators can be computed. As an example, we give the complete formula for $ langle phi(x_1)^{n},phi(x_2)^{n},bar{phi}(x_3)^{n},bar{phi}(x_4)^{n}rangle$, which reveals an interesting structure.
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We compute correlation functions of chiral primary operators in N=2 superconformal theories at large N using a construction based on supersymmetric localization recently developed by Gerchkovitz et al. We focus on N=4 SYM as well as on superconformal QCD. In the case of N=4 we recover the free field theory results as expected due to non-renormalization theorems. In the case of superconformal QCD we study the planar expansion in the large N limit. The final correlators admit a simple generalization to a finite N formula which exactly matches the various small $N$ results in the literature.
We consider near-critical two-dimensional statistical systems with boundary conditions inducing phase separation on the strip. By exploiting low-energy properties of two-dimensional field theories, we compute arbitrary $n$-point correlation of the order parameter field. Finite-size corrections and mixed correlations involving the stress tensor trace are also discussed. As an explicit illustration of the technique, we provide a closed-form expression for a three-point correlation function and illustrate the explicit form of the long-ranged interfacial fluctuations as well as their confinement within the interfacial region.
We study the sector of large charge operators $phi^n$ ($phi$ being the complexified scalar field) in the $O(2)$ Wilson-Fisher fixed point in $4-epsilon$ dimensions that emerges when the coupling takes the critical value $gsim epsilon$. We show that, in the limit $gto 0$, when the theory naively approaches the gaussian fixed point, the sector of operators with $nto infty $ at fixed $g,n^2equiv lambda$ remains non-trivial. Surprisingly, one can compute the exact 2-point function and thereby the non-trivial anomalous dimension of the operator $phi^n$ by a full resummation of Feynman diagrams. The same result can be reproduced from a saddle point approximation to the path integral, which partly explains the existence of the limit. Finally, we extend these results to the three-dimensional $O(2)$-symmetric theory with $(bar{phi},phi)^3$ potential.
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.
We compare calculations of the three-point correlation functions of BMN operators at the one-loop (next-to-leading) order in the scalar SU(2) sector from the integrability expression recently suggested by Gromov and Vieira, and from the string field theory expression based on the effective interaction vertex by Dobashi and Yoneya. A disagreement is found between the form-factors of the correlation functions in the one-loop contributions. The order-of-limits problem is suggested as a possible explanation of this discrepancy.
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