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Register a new userOn semiclassical approximation for correlators of closed string vertex operators in AdS/CFT
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We consider the 2-point function of string vertex operators representing string state with large spin in AdS_5. We compute this correlator in the semiclassical approximation and show that it has the expected (on the basis of state-operator correspondence) form of the strong-coupling limit of the 2-point function of single trace minimal twist operators in gauge theory. The semiclassical solution representing the stationary point of the path integral with two vertex operator insertions is found to be related to the large spin limit of the folded spinning string solution by a euclidean continuation, transformation to Poincare coordinates and conformal map from cylinder to complex plane. The role of the source terms coming from the vertex operator insertions is to specify the parameters of the solution in terms of quantum numbers (dimension and spin) of the corresponding string state. Understanding further how similar semiclassical methods may work for 3-point functions may shed light on strong-coupling limit of the corresponding correlators in gauge theory as was recently suggested by Janik et al in arXiv:1002.4613.
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The non-renormalization of the 3-point functions $tr X^{k_1} tr X^{k_2} tr X^{k_3}$ of chiral primary operators in N=4 super-Yang-Mills theory is one of the most striking facts to emerge from the AdS/CFT correspondence. A two-fold puzzle appears in the extremal case, e.g. k_1 = k_2 + k_3. First, the supergravity calculation involves analytic continuation in the k_i variables to define the product of a vanishing bulk coupling and an infinite integral over AdS. Second, extremal correlators are uniquely sensitive to mixing of the single-trace operators $tr X^k$ with protected multi-trace operators in the same representation of SU(4). We show that the calculation of extremal correlators from supergravity is subject to the same subtlety of regularization known for the 2-point functions, and we present a careful method which justifies the analytic continuation and shows that supergravity fields couple to single traces without admixture. We also study extremal n-point functions of chiral primary operators, and argue that Type IIB supergravity requires that their space-time form is a product of n-1 two-point functions (as in the free field approximation) multiplied by a non-renormalized coefficient. This non-renormalization property of extremal n-point functions is a new prediction of the AdS/CFT correspondence. As a byproduct of this work we obtain the cubic couplings $t phi phi$ and $s phi phi$ of fields in the dilaton and 5-sphere graviton towers of Type IIB supergravity on $AdS_5 times S^5$.
We study at quantum level correlators of supersymmetric Wilson loops with contours lying on Hopf fibers of $S^3$. In $mathcal{N}=4$ SYM theory the strong coupling analysis can be performed using the AdS/CFT correspondence and a connected classical string surface, linking two different fibers, is presented. More precisely, the string solution describes oppositely oriented fibers with the same scalar coupling and depends on an angular parameter, interpolating between a non-BPS configuration and a BPS one. The system can be thought as an alternative deformation of the ordinary antiparallel lines giving the static quark-antiquark potential, that is indeed correctly reproduced, at weak and strong coupling, as the fibers approach one another.
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.
We study near-extremal n-point correlation functions of chiral primary operators, in which the maximal scale dimension k is related to the others by k=sum_i k_i-m with m equal to or smaller than n-3. Through order g^2 in field theory, we show that these correlators are simple sums of terms each of which factors into products of lower-point correlators. Terms which contain only factors of two- and three-point functions are not renormalized, but other terms have non-vanishing order g^2 corrections. We then show that the contributing AdS exchange diagrams neatly match this factored structure. In particular, for n=4,5 precise agreement in form and coefficient is established between supergravity and the non-renormalized factored terms from field theory. On the other hand, contact diagrams in supergravity would produce a non-factored structure. This leads us to conjecture that the corresponding bulk couplings vanish, so as to achieve full agreement between the structure of these correlators in supergravity and weak-coupling field theory.
We show that string-net models provide a novel geometric method to construct invariants of mapping class group actions. Concretely, we consider string-net models for a modular tensor category ${mathcal C}$. We show that the datum of a specific commutative symmetric Frobenius algebra in the Drinfeld center $Z(mathcal{C})$ gives rise to invariant string-nets. The Frobenius algebra has the interpretation of the algebra of bulk fields of the conformal field theory in the Cardy case.
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