We calculate configuration energies of string-like membranes in M2- and M5-brane spaces. In the near horizon approximation these backgrounds reduce to $AdS_4\times S^7$ and $AdS_7\times S^4$ spaces and the dual theories are supersymmetric $SU(N)$ gauge theories, in accordance with the AdS/CFT correspondence. In this case the string-like configuration energy is identified with the quark and anti-quark energy interaction in the dual theories. Far from the horizon the dual theory is more involved but any how we were able to calculate the string-like configuration energy. For limiting regimes we find simpler solutions for which some potentials exhibit a confinement behavior while others are non-confining.
We study Wilson surface defects in 6d $\mathcal{N}=(2,0)$ superconformal field theories, engineered by semi-infinite M2-branes intersecting M5-branes. Two independent approaches are used to obtain the Wilson surface observables on the $T^2$ inside Omega-deformed $\mathbf{R}^4 \times T^2$. One approach is to compute 5d $\mathcal{N}=1^*$ instanton partition functions in the presence of Wilson lines, where the instanton corrections capture the 6d Kaluza-Klein momentum modes. The other approach is to study the elliptic genera of 2d $\mathcal{N}=(0,4)$ gauge theories, which we propose as describing…
On the D3-brane description of some 1/4 BPS Wilson loops
最近有人提出，N=4超对称杨-米尔斯理论中高维表示的威尔逊圈（或多重包裹环）可以用AdS_5 x S^5中的D膜来描述，而不是用基本弦来描述。到目前为止，仅在半BPS圆或线的情况下才发现显式D3膜解。在这里，我们提出的D3膜解决方案描述一些1/4 BPS循环。在一种情况下，其中回路被构造为由高斯矩阵模型给出，膜的作用正确地再现了威尔逊圈的期望值，包括在大λ下的所有1/N校正。和相应的弦解一样，这里我们也找到两个经典解，一个稳定，一个不稳定。不稳定的贡献指数小的修正，同意矩阵模型计算。
We study the half-BPS circular Wilson loop in ${\cal N}=4$ super Yang-Mills with orthogonal gauge group. By supersymmetric localization, its expectation value can be computed exactly from a matrix integral over the Lie algebra of $SO(N)$. We focus on the large $N$ limit and present some simple quantitative tests of the duality with type IIB string theory in $AdS_5\times \mathbb{RP}^5$. In particular, we show that the strong coupling limit of the expectation value of the Wilson loop in the spinor representation of the gauge group precisely matches the classical action of the dual string theory …
We study Wilson loops in string theory realizations of AdS/BCFT and wedge holography. The field theories are based on 3d $\mathcal N=4$ long quiver gauge theories engineered by D3, D5 and NS5 branes, and on BCFTs involving 4d $\mathcal N=4$ SYM coupled to such 3d theories. The holographic duals have geometry $AdS_4\times S^2\times S^2$ warped over a strip. We identify the holographic representation of antisymmetric Wilson loops associated with individual 3d gauge nodes in terms of probe D5-branes. The expectation values obtained holographically are matched to supersymmetric localization comput…
We use entanglement entropy to define a central charge associated to a two-dimensional defect or boundary in a conformal field theory (CFT). We present holographic calculations of this central charge for several maximally supersymmetric CFTs dual to eleven-dimensional supergravity in Anti-de Sitter space, namely the M5-brane theory with a Wilson surface defect and three-dimensional CFTs related to the M2-brane theory with a boundary. Our results for the central charge depend on a partition of the number of M2-branes, $N$, ending on the number of M5-branes, $M$. For the Wilson surface, the part…
The holographic configurations dual to Wilson loops in higher rank representations in the ABJM theory are described by branes with electric flux along their world volumes. In particular, D2 and D6 branes with electric flux play a central role as potential dual to totally symmetric and totally antisymmetric representations, respectively. We compute the spectra of excitations of these brane configurations in both, the bosonic and fermionic sectors. We highlight a number of aspects that distinguish these configurations from their D3 and D5 cousins including new peculiar mixing terms in the fluctu…
We study instanton corrections to the vacuum expectation value (VEV) of 1/6 BPS Wilson loops in ABJM theory from the Fermi gas approach. We mainly consider Wilson loops in the fundamental representation and winding Wilson loops, but we also initiate the study of Wilson loops with two boundaries. We find that the membrane instanton corrections to the Wilson loop VEV are determined by the refined topological string in the Nekrasov-Shatashvili limit, and the pole cancellation mechanism between membrane instantons and worldsheet instantons works also in the Wilson loop VEVs as in the case of the p…
We study the 1-loop dilatation operator for insertions of composite operators in a generalized Wilson loop in ${\cal N}=4$ super Yang-Mills, which interpolates between the supersymmetric Wilson-Maldacena loop and the ordinary Wilson loop with no scalar coupling. For $SO(6)$ scalar insertions, we show that the 1-loop dilatation operator is integrable for the endpoints of the interpolation, i.e. either for the Wilson-Maldacena or the ordinary Wilson loop. Moreover, we also show that integrability persists for $SU(2|3)$ insertions in the ordinary Wilson loop, even when the term making the spin ch…
We study a sector of the 5d maximally supersymmetric Yang-Mills theory on $S^5$ consisting of $1/8$-BPS Wilson loop operators contained within a great $S^3$ inside $S^5$. We conjecture that these observables are described by a 3d Chern Simons theory on $S^3$, analytically continued to a pure imaginary Chern-Simons level. Therefore, the expectation values of these 5d Wilson loops compute knot invariants. We verify this conjecture in the weakly-coupled regime from explicit Feynman diagram computations. At strong coupling, these Wilson loop operators lift to $1/8$-BPS surface operators in the 6d …
We show that generic three-dimensional $\mathcal N=2$ quiver super Chern-Simons-matter theories admit Bogomol'nyi-Prasad-Sommerfield (BPS) Drukker-Trancanelli (DT) type Wilson loops. We investigate both Wilson loops along timelike infinite straight lines in Minkowski spacetime and circular Wilson loops in Euclidean space. In Aharnoy-Bergman-Jafferis-Maldacena theory, we find that generic BPS DT type Wilson loops preserve the same number of supersymmetries as Gaiotto-Yin type Wilson loops. There are several free parameters for generic BPS DT type Wilson loops in the construction, and supersymme…
We derive Mandelstam formulae for two generalisations of the Wilson loop. In these generalisations path-ordering of Lie algebra generators is replaced by an anti-commuting one dimensional field theory along the loop. We extend the calculation to the N=1 super-Wilson loop by introducing a superpartner for the additional field.
In this paper we study Wilson loops in various representations for finite and large values of the color gauge group for supersymmetric ${\cal N}=4$ gauge theories. We also compute correlators of Wilson loops in different representations and perform a check with the dual gravitational theory.
We study the action of S-duality on half-BPS Wilson loop operators in 5d $\mathcal{N}=1$ theories. The duality is the statement that different massive deformations of a single 5d SCFT are described by different gauge theories, or equivalently that the SCFT points in parameter space of two gauge theories coincide. The pairs of dual theories that we study are realized by brane webs in type IIB string theory that are S-dual to each other. We focus on $SU(2)$ SQCD theories with $N_f \le 4$ flavors, which are self-dual, and on $SU(3)$ SQCD theories, which are dual to $SU(2)^2$ quiver theories. From…
We generalize Nakajima-Yoshioka's blowup formula to calculate the partition functions counting the spectrum of bound states to half-BPS Wilson loop operators in 5d (and 6d) supersymmetric field theories. The partition function in the presence of a Wilson loop operator on the $Ω$-background is factorized when put on the blowup $\hat{\mathbb{C}}^2$ into two Wilson loop partition functions under the localization. This structure provides a set of blowup equations for Wilson loop operators. We explain how to formulate the blowup equations and solve them to compute the partition functions of Wilson …
It is known that the expectation value of Wilson loops in the Gross-Witten-Wadia (GWW) unitary matrix model can be computed exactly at finite $N$ for arbitrary representations. We study the perturbative and non-perturbative corrections of Wilson loops in the $1/N$ expansion, either analytically or numerically using the exact result at finite $N$. As a by-product of the exact result of Wilson loops, we propose a large $N$ master field of GWW model. This master field has an interesting eigenvalue distribution. We also study the Wilson loops in large representations, called Giant Wilson loops, an…
We investigate several aspects of BPS latitude Wilson loops in gauge theories in three dimensions with $\mathcal{N}\ge 4$ supersymmetry. We derive a matrix model for the bosonic latitude Wilson loop in ABJM using supersymmetric localization, and show how to extend the computation to more general Chern-Simons-matter theories. We then define latitude type Wilson and vortex loop operators in theories without Chern-Simons terms, and explore a connection to the recently derived superalgebra defining local Higgs and Coulomb branch operators in these theories. Finally, we identify a BPS loop operator…
We study the connected correlator of 1/2 BPS winding Wilson loops in $\mathcal{N}=4$ $U(N)$ super Yang-Mills theory, where those Wilson loops are on top of each other along the same circle. We find the exact finite $N$ expression of the connected correlator of such Wilson loops. We show that the $1/N$ expansion of this exact result is reproduced from the topological recursion of Gaussian matrix model. We also study the exact finite $N$ expression of the generating function of 1/2 BPS Wilson loops in the symmetric representation.
