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Register a new userPrecision matching of circular Wilson loops and strings in AdS(5)xS(5)
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Previous attempts to match the exact N=4 super Yang-Mills expression for the expectation value of the 1/2-BPS circular Wilson loop with the semiclassical AdS(5)xS(5) string theory prediction were not successful at the first subleading order. There was a missing prefactor ~ lambda^(-3/4) which could be attributed to the unknown normalization of the string path integral measure. Here we resolve this problem by computing the ratio of the string partition functions corresponding to the circular Wilson loop and the special 1/4-supersymmetric latitude Wilson loop. The fact that the latter has a trivial expectation value in the gauge theory allows us to relate the prefactor to the contribution of the three zero modes of the transverse fluctuation operator in the 5-sphere directions.
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We study the strong coupling behaviour of $1/4$-BPS circular Wilson loops (a family of latitudes) in ${cal N}=4$ Super Yang-Mills theory, computing the one-loop corrections to the relevant classical string solutions in AdS$_5times$S$^5$. Supersymmetric localization provides an exact result that, in the large t Hooft coupling limit, should be reproduced by the sigma-model approach. To avoid ambiguities due to the absolute normalization of the string partition function, we compare the $ratio$ between the generic latitude and the maximal 1/2-BPS circle: Any measure-related ambiguity should simply cancel in this way. We use Gelfand-Yaglom method to calculate the relevant functional determinants, that present some complications with respect to the standard circular case. After a careful numerical evaluation of our final expression we still find disagreement with the localization answer: The difference is encoded into a precise remainder function. We comment on the possible origin and resolution of this discordance.
The 1/2-BPS Wilson loop in $mathcal{N}=4$ supersymmetric Yang-Mills theory is an important and well-studied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the large-rank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with $AdS_2 times S^2$ and $AdS_2 times S^4$ worldvolume geometries, ending at the $AdS_5$ boundary along a one-dimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large $N$ limit exactly as a function of the t Hooft coupling. The results are given by simple integrals of polynomials that resemble the $Q$-functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three- and four-point functions from perturbation theory on the D-branes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.
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 study the correlation function of two circular Wilson loops at strong coupling in N=4 super Yang-Mills theory. Using the AdS/CFT correspondence, the problem maps to finding the minimal surface between two circles defined on the boundary of AdS, and the fluctuations around the classical solution in AdS_5 x S^5. At the classical level, we derive the string solution in H_3 x S^1 explicitly, and focus on properties such as stability and phase transition. Furthermore, a computation of the associated algebraic curve is given. At the quantum level, the one-loop partition function is constructed by introducing quadratic bosonic and fermionic fluctuations around the classical solution, embedded in AdS_5 x S^5. We find an analytic, formal expression for the partition function in terms of an infinite product by employing the Gelfand-Yaglom method and supersymmetric regularization. We regulate the expression and evaluate the partition function numerically.
We compute the one-loop world-sheet correction to partition function of $AdS_5 times S^5$ superstring that should be representing $k$-fundamental circular Wilson loop in planar limit. The 2d metric of the minimal surface ending on $k$-wound circle at the boundary is that of a cone of $AdS_2$ with deficit $2pi (1-k)$. We compute determinants of 2d fluctuation operators by first constructing heat kernels of scalar and spinor Laplacians on the cone using the Sommerfeld formula. The final expression for the k-dependent part of the one-loop correction has simple integral representation but is different from earlier results.
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