arXiv 0806.41912008-06hep-th

Spectral curves, emergent geometry, and bubbling solutions for Wilson loops

Takuya Okuda, Diego Trancanelli

备注：: 27 pages, 2 figures; v2: references added
发表信息：: JHEP 0809:050,2008
DOI：: 10.1088/1126-6708/2008/09/050

英文摘要：

We study the supersymmetric circular Wilson loops of N=4 super Yang-Mills in large representations of the gauge group. In particular, we obtain the spectral curves of the matrix model which captures the expectation value of the loops. These spectral curves are then proven to be precisely the hyperelliptic surfaces that characterize the bubbling solutions dual to the Wilson loops, thus yielding an example of a geometry emerging from an eigenvalue distribution. We finally discuss the Wilson loop expectation value from the matrix model and from supergravity.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Entanglement entropy of Wilson surfaces from bubbling geometries in M-theory

We consider solutions of eleven-dimensional supergravity constructed in [1,2] that are half-BPS, locally asymptotic to $AdS_7\times S^4$ and are the holographic dual of heavy Wilson surfaces in the six-dimensional $(2,0)$ theory. Using these bubbling solutions we calculate the holographic entanglement entropy for a spherical entangling surface in the presence of a planar Wilson surface. In addition, we calculate the holographic stress tensor and, by evaluating the on-shell supergravity action, the expectation value of the Wilson surface operator.

2015-07-15hep-th

Strings in Bubbling Geometries and Dual Wilson Loop Correlators

We consider a fundamental string in a bubbling geometry of arbitrary genus dual to a half-supersymmetric Wilson loop in a general large representation $\mathbf{R}$ of the $SU(N)$ gauge group in ${\cal N}=4$ Supersymmetric Yang-Mills. We demonstrate, under some mild conditions, that the minimum value of the string classical action for a bubbling geometry of arbitrary genus precisely matches the correlator of a Wilson loop in the fundamental representation and one in a general large representation. We work out the case in which the large representation is given by a rectangular Young Tableau, co…

2017-12-22hep-th

A prediction for bubbling geometries

We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.

2008-02-11hep-th

Wilson loop correlators at strong coupling: from matrices to bubbling geometries

We compute at strong coupling the large N correlation functions of supersymmetric Wilson loops in large representations of the gauge group with local operators of N=4 super Yang-Mills. The gauge theory computation of these correlators is performed using matrix model techniques. We show that the strong coupling correlator of the Wilson loop with the stress tensor computed using the matrix model exactly matches the semiclassical computation of the correlator of the 't Hooft loop with the stress tensor, providing a non-trivial quantitative test of electric-magnetic duality of N=4 super Yang-Mills…

2009-04-28hep-th

Bubbling Geometries for Half BPS Wilson lines

We consider the supergravity backgrounds that correspond to supersymmetric Wilson line operators in the context of AdS/CFT correspondence. We study the gravitino and dilatino conditions of the IIB supergravity under the appropriate ansatz, and obtain some necessary conditions for a supergravity background that preserves the same symmetry as the supersymmetric Wilson lines. The supergravity solutions are characterized by continuous version of maya diagrams. This diagram is related to the eigenvalue distribution of the Gaussian matrix model. We also consider the similar backgrounds of the 11-dim…

2006-05-18hep-th

Bubbling Calabi-Yau geometry from matrix models

We study bubbling geometry in topological string theory. Specifically, we analyse Chern-Simons theory on both the 3-sphere and lens spaces in the presence of a Wilson loop insertion of an arbitrary representation. For each of these three manifolds we formulate a multi-matrix model whose partition function is the vev of the Wilson loop and compute the spectral curve. This spectral curve is the reduction to two dimensions of the mirror to a Calabi-Yau threefold which is the gravitational dual of the Wilson loop insertion. For lens spaces the dual geometries are new. We comment on a similar matri…

2008-02-01hep-th

更多相关论文收起更多论文

Emergent bubbling geometries in gauge theories with SU(2|4) symmetry

We study the gauge/gravity duality between bubbling geometries in type IIA supergravity and gauge theories with SU(2|4) symmetry, which consist of N=4 super Yang-Mills on $R\times S^3/Z_k$, N=8 super Yang-Mills on $R\times S^2$ and the plane wave matrix model. We show that the geometries are realized as field configurations in the strong coupling region of the gauge theories. On the gravity side, the bubbling geometries can be mapped to electrostatic systems with conducting disks. We derive integral equations which determine the charge densities on the disks. On the gauge theory side, we obtai…

2014-07-05hep-th

Emergent bubbling geometries in the plane wave matrix model

The gravity dual geometry of the plane wave matrix model is given by the bubbling geometry in the type IIA supergravity, which is described by an axially symmetric electrostatic system. We study a quarter BPS sector of the plane wave matrix model in terms of the localization method and show that this sector can be mapped to a one-dimensional interacting Fermi gas system. We find that the mean-field density of the Fermi gas can be identified with the charge density in the electrostatic system in the gravity side. We also find that the scaling limits in which the dual geometry reduces to the D2-…

2014-03-10hep-th

Wilson Loops, Geometric Transitions and Bubbling Calabi-Yau's

Motivated by recent developments in the AdS/CFT correspondence, we provide several alternative bulk descriptions of an arbitrary Wilson loop operator in Chern-Simons theory. Wilson loop operators in Chern-Simons theory can be given a description in terms of a configuration of branes or alternatively anti-branes in the resolved conifold geometry. The representation of the Wilson loop is encoded in the holonomy of the gauge field living on the dual brane configuration. By letting the branes undergo a new type of geometric transition, we argue that each Wilson loop operator can also be described …

2007-02-07hep-thmath.DG

线缺陷鼓泡几何的激发

Excitations of bubbling geometries for line defects

该研究通过大N极限下的超对称指标，计算了半BPS威尔逊线对应的鼓泡几何上的量子涨落谱，发现多粒子激发谱与有限域上一般线性群的共轭类数目一致，并揭示了新的渐近态简并类。

2023-11-23hep-th

气泡虫洞与矩阵模型

Bubbling wormholes and matrix models

Ghent University（根特大学）；ETH Zurich（苏黎世联邦理工学院）；CNRS, École polytechnique, Institut Polytechnique de Paris（法国国家科学研究中心，巴黎综合理工学院，巴黎理工学院）

本文通过多重U(N)超Yang-Mills理论中的半BPS Wilson环的表示求和，探讨了与热场双态类似的构造，并提出这些构造的反物质双正是多覆盖的AdS5×S5气泡虫洞几何。

2026-05-12hep-th

Emergent geometry from field theory: Wilson's renormalization group revisited

We find a geometrical description from a field theoretical setup based on Wilson's renormalization group in real space. We show that renormalization group equations of coupling parameters encode the metric structure of an emergent curved space, regarded to be an Einstein equation for the emergent gravity. Self-consistent equations of local order-parameter fields with an emergent metric turn out to describe low energy dynamics of a strongly coupled field theory, analogous to the Maxwell equation of the Einstein-Maxwell theory in the AdS$_{d+2}$/CFT$_{d+1}$ duality conjecture. We claim that the …

2016-04-18cond-mat.str-elhep-th

涌现的AdS几何与黑洞热力学从功能重整化群

Emergent $\text{AdS}_{d+1}$ Geometry from Functional Renormalization Group via Bulk Metric Reconstruction

POSTECH（浦项工科大学）；Asia Pacific Center for Theoretical Physics (APCTP)（亚太理论物理中心）

该研究通过功能重整化群框架，提出非微扰的双生描述，揭示了O(N)向量模型在欧几里得空间中的AdS几何结构，并证明了霍金温度与边界场论温度的一致性，以及黑洞热力学第一定律的满足。

2026-07-28hep-th

Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: Matrix Model and Classical String

We study the large charge sector of the defect CFT defined by the half-BPS Wilson loop in planar $\mathcal{N}=4$ 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 $J/\sqrtλ$ 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 …

2022-04-06hep-th

Wilson Loops in Non-Compact U(1) Gauge Theories at Criticality

We study the properties of Wilson loops in three dimensional non-compact U(1) gauge theories with global abelian symmetries. We use duality in the continuum and on the lattice, to argue that close to the critical point between the Higgs and Coulomb phases, all correlators of the Wilson loops are periodic functions of the Wilson loop charge, Q. The period depends on the global symmetry of the theory, which determines the magnetic flux carried by the dual particles. For single flavour scalar electrodynamics, the emergent period is Q = 1. In the general case of N complex scalars with a U(1)^{N-1}…

2007-10-19hep-lathep-phhep-th

通过cohomotopy中的磁通量子化对Chern-Simons威尔逊环进行重整化

Renormalization of Chern-Simons Wilson Loops via Flux Quantization in Cohomotopy

Mathematics Program and Center for Quantum and Topological Systems, New York University Abu Dhabi（纽约大学阿布扎比分校数学项目及量子与拓扑系统中心）

本文通过cohomotopy中的磁通量子化方法，揭示了Chern-Simons理论中威尔逊环观测量的重整化选择，并探讨其在拓扑有序量子材料中的应用。

2025-10-20cond-mat.str-elhep-thmath-ph

Supersymmetric 4d gauge theories and Integrability

This thesis is devoted to some particular aspects of integrability in $4d$ SUSY gauge theories. Taking advantage of the integrable structures emergent in the theory, non-local observables such as null polygonal Wilson loops are studied in $4d$ planar $\mathcal{N}=4$ Super Yang-Mills. Their duality with the $4d$ gluon scattering amplitudes makes the analysis even more interesting. The so-called \emph{Pentagon approach}, an application of the Operator Product Expansion (OPE) method to the null polygonal Wilsol loops, makes possible a non-perturbative evaluation of these objects. They are recast …

2018-07-25hep-th