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Register a new userExact Large R-charge Correlators in ABJM Theory
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Authors
Tanay K. Dey
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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.
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In this paper we study the Bremsstrahlung functions for the 1/6 BPS and the 1/2 BPS Wilson lines in ABJM theory. First we use a superconformal defect approach to prove a conjectured relation between the Bremsstrahlung functions associated to the geometric ($B^{varphi}_{1/6}$) and R-symmetry ($B^{theta}_{1/6}$) deformations of the 1/6 BPS Wilson line. This result, non-trivially following from a defect supersymmetric Ward identity, provides an exact expression for $B^{theta}_{1/6}$ based on a known result for $B^{varphi}_{1/6}$. Subsequently, we explore the consequences of this relation for the 1/2 BPS Wilson line and, using the localization result for the multiply wound Wilson loop, we provide an exact closed form for the corresponding Bremsstrahlung function. Interestingly, for the comparison with integrability, this expression appears particularly natural in terms of the conjectured interpolating function $h(lambda)$. During the derivation of these results we analyze the protected defect supermultiplets associated to the broken symmetries, including their two- and three-point correlators.
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.
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.
We present the three-loop calculation of the Bremsstrahlung function associated to the 1/2-BPS cusp in ABJM theory, including color subleading corrections. Using the BPS condition we reduce the computation to that of a cusp with vanishing angle. We work within the framework of heavy quark effective theory (HQET) that further simplifies the analytic evaluation of the relevant cusp anomalous dimension in the near-BPS limit. The result passes nontrivial tests, such as exponentiation, and is in agreement with the conjecture made in [1] for the exact expression of the Bremsstrahlung function, based on the relation with fermionic latitude Wilson loops.
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.
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