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Register a new userCorrelators Of Operators with a Large R-charge
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Correlation functions of operators with a conformal dimension of O(N^2) are not well approximated by the planar limit. The non-planar diagrams, which in the bulk spacetime correspond to string loop corrections, are enhanced by huge combinatorial factors. In this article we show how these loop corrections can be resummed. As a typical example of our results, in the half-BPS background of M maximal giant gravitons we find the usual 1/N expansion is replaced by a 1/(M+N) expansion. Further, we find that there is a simple exact relationship between amplitudes computed in the trivial background and amplitudes computed in the background of M maximal giant gravitons. Finally, we also find strong evidence for the BMN-type sectors suggested in arXiv:0801.4457. The decoupling limit of arXiv:0801.4457 captures the decoupled low energy world volume theory of the intersecting giant graviton system and this theory is weakly coupled even when the original N=4 super Yang-Mills theory is strongly coupled.
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We construct a class of operators, given by Schur polynomials, in ABJM theory. By computing two point functions at finite $N$ we confirm these are diagonal for this class of operators in the free field limit. We also calculate exact three and multi point correlators in the zero coupling limit. Finally, we consider a particular nontrivial background produced by an operator with an $R$-charge of $O(N^2$. We show that the nonplanar corrections (which can no longer be neglected, even at large $N$) can be resummed to give a $1/(N+M)$ expansion for correlators computed in this background.
Using supersymmetric localization, we study the sector of chiral primary operators $({rm Tr} , phi^2 )^n$ with large $R$-charge $4n$ in $mathcal{N}=2$ four-dimensional superconformal theories in the weak coupling regime $grightarrow 0$, where $lambdaequiv g^2n$ is kept fixed as $ntoinfty $, $g$ representing the gauge theory coupling(s). In this limit, correlation functions $G_{2n}$ of these operators behave in a simple way, with an asymptotic behavior of the form $G_{2n}approx F_{infty}(lambda) left(frac{lambda}{2pi e}right)^{2n} n^alpha $, modulo $O(1/n)$ corrections, with $alpha=frac{1}{2} mathrm{dim}(mathfrak{g})$ for a gauge algebra $mathfrak{g}$ and a universal function $F_{infty}(lambda)$. As a by-product we find several new formulas both for the partition function as well as for perturbative correlators in ${cal N}=2$ $mathfrak{su}(N)$ gauge theory with $2N$ fundamental hypermultiplets.
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.
We calculate all components of thermal R-current correlators from AdS/CFT correspondence for non-zero momentum and energy. In zero momentum limit, we find an analytic expression for the components Gxx(Gyy). The dielectric function of strong coupling is also presented and compared with that in weak coupling.
For SCFTs with an $SU(2)$ R-symmetry, we determine the superconformal blocks that contribute to the four-point correlation function of a priori distinct half-BPS superconformal primaries as an expansion in terms of the relevant bosonic conformal blocks. This is achieved by using the superconformal Casimir equation and the superconformal Ward identity to fix the coefficients of the bosonic blocks uniquely in a dimension-independent way. In addition we find that many of the resulting coefficients are related through a web of linear transformations of the conformal data.
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