Giant Wilson loops and AdS2/dCFT1

Abstract

The 1/2-BPS Wilson loop in $$ \mathcal{N} $$ 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 AdS2× S2 and AdS2× S4 worldvolume geometries, ending at the AdS5 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.

Wilson loops in $$ \mathcal{N} $$ = 4 SO(N) SYM and D-branes in AdS5 × ℝℙ5

“…[26,27,[29][30][31]). Likewise, defect CFT correlators on Wilson loops in (anti)symmetric representations and their duality to fluctuations of the D3 and D5-branes were recently studied in detail in [32]. It would be interesting to perform similar defect CFT analyses for SO(N ) gauge theory and in particular for the spinor representation, which is a unique feature of orthogonal groups.…”

“…To review the basic facts about those D-brane solutions, it is convenient to use the following AdS 2 × S 2 slicing of the AdS 5 metric (see e.g. [32] for more details on the form of the brane solutions and their actions using these coordinates)…”

“…The D3-brane on-shell action, obtained by summing the DBI and Wess-Zumino contributions, and supplemented by a boundary term implementing a Legendre transform on the gauge field, yields [15] (see [32] for the calculation in the coordinates used here)…”

The topological line of ABJ(M) theory

“…A natural generalization of the present investigation would concern the construction of topological operators inserted into the 1/2 BPS Wilson line. Defect conformal field theories supported on the 1/2 BPS Wilson line have been studied in four-dimensional N = 4 SYM [48,49] and its topological sector has been extensively studied in a series of papers [50][51][52]. The defect conformal field theory related to the 1/2 BPS Wilson line in ABJ(M) theory has been examined in [53], where it has been shown that, at variance with the four-dimensional case, the displacement supermultiplet does not admit a topological sector.…”

Open fishchain in N = 4 Supersymmetric Yang-Mills Theory

“…Finally it would be interesting to look at other examples of integrable boundary conditions in N = 4 SYM. These include determinant operators [83][84][85][86] (and references therein) and giant Wilson loops [87].…”