skip to main content

Title: Dressing bulk fields in AdS3
A bstract We study a set of CFT operators suitable for reconstructing a charged bulk scalar field ϕ in AdS 3 (dual to an operator $$ \mathcal{O} $$ O of dimension ∆ in the CFT) in the presence of a conserved spin- n current in the CFT. One has to sum a tower of smeared non-primary scalars $$ {\partial}_{+}^m{J}^{(m)} $$ ∂ + m J m , where J ( m ) are primaries with twist ∆ and spin m built from $$ \mathcal{O} $$ O and the current. The coefficients of these operators can be fixed by demanding that bulk correlators are well-defined: with a simple ansatz this requirement allows us to calculate bulk correlators directly from the CFT. They are built from specific polynomials of the kinematic invariants up to a freedom to make field redefinitions. To order 1/ N this procedure captures the dressing of the bulk scalar field by a radial generalized Wilson line.
Award ID(s):
Publication Date:
Journal Name:
Journal of High Energy Physics
Sponsoring Org:
National Science Foundation
More Like this
  1. A bstract We study 2-point correlation functions for scalar operators in position space through holography including bulk cubic couplings as well as higher curvature couplings to the square of the Weyl tensor. We focus on scalar operators with large conformal dimensions. This allows us to use the geodesic approximation for propagators. In addition to the leading order contribution, captured by geodesics anchored at the insertion points of the operators on the boundary and probing the bulk geometry thoroughly studied in the literature, the first correction is given by a Witten diagram involving both the bulk cubic coupling and the higher curvature couplings. As a result, this correction is proportional to the VEV of a neutral operator O k and thus probes the interior of the black hole exactly as in the case studied by Grinberg and Maldacena [13]. The form of the correction matches the general expectations in CFT and allows to identify the contributions of T n O k (being T n the general contraction of n energy-momentum tensors) to the 2-point function. This correction is actually the leading term for off-diagonal correlators (i.e. correlators for operators of different conformal dimension), which can then be computed holographically in thismore »way.« less
  2. A bstract We study the large charge sector of the defect CFT defined by the half-BPS Wilson loop in planar N = 4 supersymmetric Yang-Mills theory. Specifically, we consider correlation functions of two large charge insertions and several light insertions in the double-scaling limit where the ’t Hooft coupling λ and the large charge J are sent to infinity, with the ratio J/ $$ \sqrt{\lambda } $$ λ held fixed. They are holographically dual to the expectation values of light vertex operators on a classical string solution with large angular momentum, which we evaluate in the leading large J limit. We also compute the two-point function of large charge insertions by evaluating the on-shell string action, supplemented by the boundary terms that generalize the one introduced by Drukker, Gross and Ooguri for the Wilson loop without insertions. For a special class of correlation functions, we reproduce the string results from field theory by using supersymmetric localization. The results are given by correlation functions in an “emergent” matrix model whose matrix size is proportional to J and whose spectral curve coincides with that of the classical string. Similar matrix models appeared in the study of extremal correlators in rank-1 $$ \mathcal{N}more »$$ N = 2 superconformal field theories, but our results hold also for non-extremal cases.« less
  3. A bstract We study monodromy defects in O ( N ) symmetric scalar field theories in d dimensions. After a Weyl transformation, a monodromy defect may be described by placing the theory on S 1 × H d− 1 , where H d− 1 is the hyperbolic space, and imposing on the fundamental fields a twisted periodicity condition along S 1 . In this description, the codimension two defect lies at the boundary of H d− 1 . We first study the general monodromy defect in the free field theory, and then develop the large N expansion of the defect in the interacting theory, focusing for simplicity on the case of N complex fields with a one-parameter monodromy condition. We also use the ϵ -expansion in d = 4 − ϵ , providing a check on the large N approach. When the defect has spherical geometry, its expectation value is a meaningful quantity, and it may be obtained by computing the free energy of the twisted theory on S 1 × H d− 1 . It was conjectured that the logarithm of the defect expectation value, suitably multiplied by a dimension dependent sine factor, should decrease under a defect RGmore »flow. We check this conjecture in our examples, both in the free and interacting case, by considering a defect RG flow that corresponds to imposing alternate boundary conditions on one of the low-lying Kaluza-Klein modes on H d− 1 . We also show that, adapting standard techniques from the AdS/CFT literature, the S 1 × H d− 1 setup is well suited to the calculation of the defect CFT data, and we discuss various examples, including one-point functions of bulk operators, scaling dimensions of defect operators, and four-point functions of operator insertions on the defect.« less
  4. A bstract We compute 1 /λ corrections to the four-point functions of half-BPS operators in SU( N ) $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory at large N and large ’t Hooft coupling λ = $$ {g}_{\mathrm{YM}}^2N $$ g YM 2 N using two methods. Firstly, we relate integrals of these correlators to derivatives of the mass deformed S 4 free energy, which was computed at leading order in large N and to all orders in 1 /λ using supersymmetric localization. Secondly, we use AdS/CFT to relate these 1 /λ corrections to higher derivative corrections to supergravity for scattering amplitudes of Kaluza-Klein scalars in IIB string theory on AdS 5 × S 5 , which in the flat space limit are known from worldsheet calculations. These two methods match at the order corresponding to the tree level R 4 interaction in string theory, which provides a precise check of AdS/CFT beyond supergravity, and allow us to derive the holographic correlators to tree level D 4 R 4 order. Combined with constraints from [1], our results can be used to derive CFT data to one-loop D 4 R 4 order. Finally, we use AdS/CFT to fix these correlators in themore »limit where N is taken to be large while g YM is kept fixed. In this limit, we present a conjecture for the small mass limit of the S 4 partition function that includes all instanton corrections and is written in terms of the same Eisenstein series that appear in the study of string theory scattering amplitudes.« less
  5. A bstract We study which bulk couplings contribute to the S 3 free energy F ( $$ \mathfrak{m} $$ m ) of three-dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories with holographic duals, potentially deformed by boundary real-mass parameters m. In particular, we show that F ( $$ \mathfrak{m} $$ m ) is independent of a large class of bulk couplings that include non-chiral F-terms and all D-terms. On the other hand, in general, F ( $$ \mathfrak{m} $$ m ) does depend non-trivially on bulk chiral F-terms, such as prepotential interactions, and on bulk real-mass terms. These conclusions can be reached solely from properties of the AdS super-algebra, $$ \mathfrak{osp} $$ osp (2|4). We also consider massive vector multiplets in AdS, which in the dual field theory correspond to long single-trace superconformal multiplets of spin zero. We provide evidence that F ( $$ \mathfrak{m} $$ m ) is insensitive to the vector multiplet mass and to the interaction couplings between the massive vector multiplet and massless ones. In particular, this implies that F ( $$ \mathfrak{m} $$ m ) does not contain information about scaling dimensions or OPE coefficients of single-trace long scalar $$ \mathcal{N} $$ Nmore »= 2 superconformal multiplets.« less