scholarly journals Surprises in the AdS algebraic curve constructions — Wilson loops and correlation functions

2012 ◽  
Vol 861 (3) ◽  
pp. 361-386 ◽  
Author(s):  
Romuald A. Janik ◽  
Paweł Laskoś-Grabowski
Keyword(s):  
Correlation Functions ◽  
Algebraic Curve ◽  
Wilson Loops

scholarly journals Giant Wilson loops and AdS2/dCFT1

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Simone Giombi ◽  
Jiaqi Jiang ◽  
Shota Komatsu
Keyword(s):  
Correlation Functions ◽  
Wilson Loop ◽  
Wilson Loops ◽  
One Dimensional ◽  
Yang Mills ◽  
Large Rank ◽  
Hooft Coupling ◽  
Multiple Integrals ◽  
The Difference ◽  
Selection Of

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.

scholarly journals 3d $$ \mathcal{N} $$ = 2 Chern-Simons-matter theory, Bethe ansatz, and quantum K -theory of Grassmannians

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Kazushi Ueda ◽  
Yutaka Yoshida
Keyword(s):  
Bethe Ansatz ◽  
Correlation Functions ◽  
Quantum Cohomology ◽  
Frobenius Algebra ◽  
Wilson Loops ◽  
Small Quantum ◽  
Starting Point ◽  
Matter Theory ◽  
Verlinde Algebras ◽  
Chern Simons

Abstract We study a correspondence between 3d $$ \mathcal{N} $$ N = 2 topologically twisted Chern-Simons-matter theories on S1× Σg and quantum K -theory of Grassmannians. Our starting point is a Frobenius algebra depending on a parameter β associated with an algebraic Bethe ansatz introduced by Gorbounov-Korff. They showed that the Frobenius algebra with β = −1 is isomorphic to the (equivariant) small quantum K -ring of the Grassmannian, and the Frobenius algebra with β = 0 is isomorphic to the equivariant small quantum cohomology of the Grassmannian. We apply supersymmetric localization formulas to the correlation functions of supersymmetric Wilson loops in the Chern-Simons-matter theory and show that the algebra of Wilson loops is isomorphic to the Frobenius algebra with β = −1. This allows us to identify the algebra of Wilson loops with the quantum K - ring of the Grassmannian. We also show that correlation functions of Wilson loops on S1× Σg satisfy the axiom of 2d TQFT. For β = 0, we show the correspondence between an A-twisted GLSM, the Frobenius algebra for β = 0, and the quantum cohomology of the Grassmannian. We also discuss deformations of Verlinde algebras, omega-deformations, and the K -theoretic I -functions of Grassmannians with level structures.

HOLOGRAPHY OF ROTATING DUAL GIANT WILSON LOOPS

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2267-2268
Author(s):  
AKITSUGU MIWA ◽  
YOSKE SUMITOMO ◽  
KENTAROH YOSHIDA
Keyword(s):  
Correlation Functions ◽  
Wilson Loops ◽  
Wick Rotation ◽  
Expectation Values ◽  
Giant Graviton

We briefly review a tunneling picture of rotating D3-brane solutions. By applying the "double Wick rotation" to the Lorentzian solutions, we construct Euclidean solutions. The solutions are composed of dual giant gravitons and spike D3-brane solutions, and their classical actions reproduce expectation values of the k-th symmetric Wilson loops as well as correlation functions of dual giant graviton operators as expected.

scholarly journals Holographic correlation functions of hexagon Wilson loops with one local operator

2013 ◽  
Vol 726 (1-3) ◽  
pp. 417-421
Author(s):  
Rafael Hernández ◽  
Juan Miguel Nieto
Keyword(s):  
Correlation Functions ◽  
Local Operator ◽  
Wilson Loops

scholarly journals From correlation functions to Wilson loops

2011 ◽  
Vol 2011 (9) ◽  
Author(s):  
Luis F. Alday ◽  
Burkhard Eden ◽  
Gregory P. Korchemsky ◽  
Juan Maldacena ◽  
Emery Sokatchev
Keyword(s):  
Correlation Functions ◽  
Wilson Loops
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