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Register a new userGiant Wilson Loops and AdS$_2$/dCFT$_1$
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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.
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We aim at formulating a higher-spin gravity theory around AdS$_2$ relevant for holography. As a first step, we investigate its kinematics by identifying the low-dimensional cousins of the standard higher-dimensional structures in higher-spin gravity such as the singleton, the higher-spin symmetry algebra, the higher-rank gauge and matter fields, etc. In particular, the higher-spin algebra is given here by $hs[lambda]$ and parameterized by a real parameter $lambda$. The singleton is defined to be a Verma module of the AdS$_2$ isometry subalgebra $so(2,1) subset hs[lambda]$ with conformal weight $Delta = frac{1pmlambda}{2},$. On the one hand, the spectrum of local modes is determined by the Flato-Fronsdal theorem for the tensor product of two such singletons. It is given by an infinite tower of massive scalar fields in AdS$_2$ with ascending masses expressed in terms of $lambda$. On the other hand, the higher-spin fields arising through the gauging of $hs[lambda]$ algebra do not propagate local degrees of freedom. Our analysis of the spectrum suggests that AdS$_2$ higher-spin gravity is a theory of an infinite collection of massive scalars with fine-tuned masses, interacting with infinitely many topological gauge fields. Finally, we discuss the holographic CFT$_1$ duals of the kinematical structures identified in the bulk.
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.
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.
A 0+1-dimensional candidate theory for the CFT$_1$ dual to AdS$_2$ is discussed. The quantum mechanical system does not have a ground state that is invariant under the three generators of the conformal group. Nevertheless, we show that there are operators in the theory that are not primary, but whose non-primary character conspires with the non-invariance of the vacuum to give precisely the correlation functions in a conformally invariant theory.
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.
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