We localize the loop equation of large-N YM theory in the ASD variables on a critical equation for an effective action by means of homological methods as opposed to the cohomological localization of equivariantly closed forms in local field theory. Our localization occurs for some special simple quasi BPS Wilson loops, that have no perimeter divergence and no cusp anomaly for backtracking cusps, in a partial Eguchi-Kawai reduction from four to two dimensions of the non-commutative theory in the limit of infinite non-commutativity and in a lattice regularization in which the ASD integration variables live at the points of the lattice, thus implying an embedding of parabolic Higgs bundles in the YM functional integral. We find that the beta function of the effective action is saturated by the non-commutative ASD vortices of the EK reduction. An exact canonical beta function of NSVZ type that reproduces the universal first and second perturbative coefficients follows by the localization on vortices. Finally we argue that a scheme can be found in which the canonical coupling coincides with the physical charge between static quark sources in the large-N limit and we compare our theoretical calculation with some numerical lattice result.
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.
We construct new families of 1/4 BPS Wilson loops in circular quiver $\mathcal N=4$ superconformal Chern-Simons-matter (SCSM) theories in three dimensions. They are defined as the holonomy of superconnections that contain non-trivial couplings to scalar and fermions, and cannot be reduced to block-diagonal matrices. Consequently, the new operators cannot be written in terms of double-node Wilson loops, as the ones considered so far in the literature. For particular values of the couplings the superconnection becomes block-diagonal and we recover the known fermionic 1/4 and 1/2 BPS Wilson loops…
In $\mathcal N \geq 2$ superconformal Chern-Simons-matter theories we construct the infinite family of Bogomol'nyi-Prasad-Sommerfield (BPS) Wilson loops featured by constant parametric couplings to scalar and fermion matter, including both line Wilson loops in Minkowski spacetime and circle Wilson loops in Euclidean space. We find that the connection of the most general BPS Wilson loop cannot be decomposed in terms of double-node connections. Moreover, if the quiver contains triangles, it cannot be interpreted as a supermatrix inside a superalgebra. However, for particular choices of the param…
BPS Wilson loops in Minkowski spacetime and Euclidean space
我们给出了类空BPS威尔逊圈在闵可夫斯基时空中不存在的证据。我们证明了闵可夫斯基时空中的类空威尔逊圈不能保持任何超对称性，在$d = 4$ $\mathcal N = 4$ super Yang-Mills理论，$d = 3$ $\mathcal N = 2$ super Chern-Simons-matter理论和$d = 3$ $\mathcal N = 6$ Aharony-Bergman-Jafferis-Maldacena理论中。我们不仅使用无限的直线和圆作为例子来证明这一点，而且我们也给出了一般曲线的证明。我们把这归因于旋量的现实条件的冲突。然而，类空威尔逊圈确实存在于欧几里得空间中。存在沿无限直线的BPS威尔逊圈和圆形BPS威尔逊圈。这是因为在Wick旋转之后，旋量的现实条件消失了。从AdS/CFT对应关系来看，这一结果是合理的。
The generating functions for the Wilson loops in the symmetric and antisymmetric representations of the gauge group $U(N)$ are expressed in terms of the connected correlators of multiply-wound Wilson loops, using ingredients from the representation theory of the symmetric group. This provides a proof of a recent observation by Okuyama. As a by-product, we present a new calculation of the connected 2-point correlator of multiply-wound Wilson loops at leading order in $1/N$.
We study the possible BPS Wilson loops in three-dimensional ${\cal N}=4$ Chern-Simons-matter theory which involve only the gauge field and bilinears of the scalars. Previously known examples are the analogues of the Gaiotto-Yin loops preserving four supercharges and "latitude" loops preserving two. We carry out a careful classification and find, in addition, loops preserving three supercharges, further inequivalent classes of loops preserving two supercharges and loops preserving a single supercharge. For each of the classes of loops, we present a representative example and analyse their full …
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 compute correlation functions of protected primaries on the $1/2$-BPS Wilson loop in ${\cal N}$ = 4 super Yang-Mills theory at weak coupling. We first perform direct perturbative computation at one loop in the planar limit and present explicit formulae for general two-, three- and four-point functions. The results for two- and three-point functions as well as four-point functions in special kinematics are in perfect agreement with the localization computation performed in arXiv:1802.05201. We then analyze the results in view of the integrability-based approach called "hexagonalization", whi…
We study correlation functions of local operator insertions on the 1/2-BPS Wilson line in ${\cal N}=4$ super Yang-Mills theory. These correlation functions are constrained by the 1d superconformal symmetry preserved by the 1/2-BPS Wilson line and define a defect CFT$_1$ living on the line. At strong coupling, a set of elementary operator insertions with protected scaling dimensions correspond to fluctuations of the dual fundamental string in AdS$_5 \times S^5$ ending on the line at the boundary and can be thought of as light fields propagating on the AdS$_2$ worldsheet. We use AdS/CFT techniqu…
We consider the 1/2 BPS circular Wilson loop in a generic N=2 SU(N) SYM theory with conformal matter content. We study its vacuum expectation value, both at finite $N$ and in the large-N limit, using the interacting matrix model provided by localization results. We single out some families of theories for which the Wilson loop vacuum expectation values approaches the N=4 result in the large-N limit, in agreement with the fact that they possess a simple holographic dual. At finite N and in the generic case, we explicitly compare the matrix model result with the field-theory perturbative expansi…
We construct for the first time Drukker-Trancanelli (DT) type fermionic Bogomolnyi-Prasad-Sommerfield (BPS) Wilson loops in four-dimensional $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver theory and $\mathcal{N}=4$ super Yang-Mills theory. The connections of these fermionic BPS Wilson loops have a supermatrix structure. We construct timelike BPS Wilson lines in Minkowski spacetime and circular BPS Wilson loops in Euclidean space. These Wilson loops involve dimensionful parameters. For generic values of parameters, they preserve one real (complex) supercharge in Lorentzian (Euclidean…
We revisit the calculation of one-loop corrections to the partition functions of a string ending on a circular or straight line in type IIB string theory on $AdS_3\times S^3 \times T^4$ supported by a mixture of 3-form fluxes depending on a parameter $q$ (with $q=0$ being R-R and $q=1$ pure NS-NS cases). Correcting earlier results in the literature, we find that the partition function depends on $q$ only through rescaled tension $T= T_0/(1-q^2)$.
Three dimensional supersymmetric field theories have large moduli spaces of circular Wilson loops preserving a fixed set of supercharges. We simplify previous constructions of such Wilson loops and amend and clarify their classification. For a generic quiver gauge theory we identify the moduli space as a quotient of $C^m$ for some $m$ by an appropriate symmetry group. These spaces are quiver varieties associated to a cover of the original quiver or a subquiver thereof. This moduli space is generically singular and at the singularities there are large degeneracies of operators which seem differ…
Recent progresses in the computation of quantum string corrections to holographic Wilson loops are extended to the case of strings in $AdS_{4}\times CP^{3}$. For this, the ratio of 1/2-BPS circular and 1/6-BPS latitude fermionic Wilson loops in ABJM is considered at strong coupling by studying the corresponding semiclassical string partition functions. Explicit evaluation of fluctuation determinants using phaseshifts and diffeomorphism invariant regulators leads to exact matching with the recent field theory proposal. Key to this computation is the choice of boundary conditions for massless fe…
Starting with some known localization (matrix model) representations for correlators involving 1/2 BPS circular Wilson loop $\cal W$ in ${\cal N}=4$ SYM theory we work out their $1/N$ expansions in the limit of large 't Hooft coupling $λ$. Motivated by a possibility of eventual matching to higher genus corrections in dual string theory we follow arXiv:2007.08512 and express the result in terms of the string coupling $g_{\rm s} \sim g^2_{\rm YM} \sim λ/N$ and string tension $T\sim \sqrt λ$. Keeping only the leading in $1/T$ term at each order in $g_{\rm s} $ we observe that while the expansion …
