Giant Wilson Loops and AdS$_2$/dCFT$_1$

Abstract

The 1/2-BPS Wilson loop in 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 × S 2 and AdS 2 × 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.

Correlators on the wall and $\mathfrak{sl}_n$ spin chain

“…Finally, there is a close relation to the results in [31,32], who also studied topological correlators in 4d MSYM, however they look at local observables on Wilson loops. Indeed, Wilson loops associated to D5 branes are also associated to Yangian embeddings in protected subsectors, which can be explained by the same Ω deformation of 6d SYM argument.…”

Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds

“…They define a set of correlators respecting the properties of a 1D CFT [31]. These physical observables have been investigated intensively in the past few years with a wide variety of methods, from string and gauge theory computations to localisation, integrability and the conformal bootstrap [17,[30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] (for less supersymmetric setups see e.g. [45][46][47]).…”

N=2 Conformal SYM theories at large N

“…When a chiral operator is inserted we can proceed as for the two-point functions in (4. 16) and find…”

“…Important achievements have been obtained in this highly symmetric context also in presence of extended objects, like the BPS Wilson loops, that preserve part of the N = 4 superconformal symmetry [5][6][7][8] and are examples of conformal defects [9][10][11][12][13][14][15][16]. Many of these results can be efficiently derived using supersymmetric localization [17,18], which allows to reduce the calculation of the partition function on a sphere S 4 and of other observables to a computation in a Gaussian matrix model.…”