# Minimal area surfaces dual to Wilson loops and the Mathieu equation

@article{Huang2016MinimalAS, title={Minimal area surfaces dual to Wilson loops and the Mathieu equation}, author={Changyu Huang and Yifei He and Martin Kruczenski}, journal={Journal of High Energy Physics}, year={2016}, volume={2016}, pages={1-26} }

A bstractThe AdS/CFT correspondence relates Wilson loops in N=4$$ \mathcal{N}=4 $$ SYM to minimal area surfaces in AdS5× S5 space. Recently, a new approach to study minimal area surfaces in AdS3 ⊂ AdS5 was discussed based on a Schroedinger equation with a periodic potential determined by the Schwarzian derivative of the shape of the Wilson loop. Here we use the Mathieu equation, a standard example of a periodic potential, to obtain a class of Wilson loops such that the area of the dual minimal…

## 16 Citations

Minimal area surfaces in AdSn+1 and Wilson loops

- Mathematics
- 2017

A bstractThe AdS/CFT correspondence relates the expectation value of Wilson loops in N$$ \mathcal{N} $$ = 4 SYM to the area of minimal surfaces in AdS5. In this paper we consider minimal area…

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- 2017

Minimal area surfaces in ending on a given curve at the boundary are dual to planar Wilson loops in SYM. In previous work it was shown that the problem of finding such surfaces can be recast as the…

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- 2017

This thesis discusses hidden symmetries within N “ 4 supersymmetric Yang– Mills theory or its AdS/CFT dual, string theory in AdS5 ˆ S. Here, we focus on the Maldacena–Wilson loop, which is a suitable…

Deformations of the circular Wilson loop and spectral (in)dependence

- PhysicsJournal of High Energy Physics
- 2019

A bstractIn this paper we study the expectation value of deformations of the circular Wilson loop in N=4$$ \mathcal{N}=4 $$ super Yang-Mills theory. The leading order deformation, known as the…

Exact results in QFT: Minimal Areas and Maximal Couplings

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- 2016

This thesis is devoted to a two-pronged study of non-perturbative quantum field theory. In Part I we focus on the four-dimensional super conformal N = 4 Yang Mills theory. We compute smooth Wilson…

Semiclassical $p$-branes in hyperbolic space.

- Mathematics
- 2020

The one-loop effects to the Dirac action of $p$-branes in a hyperbolic background from the path integral and the solution of the Wheeler-DeWitt equation are analysed. The objective of comparing the…

On the heat kernel and semiclassical $p$-branes in hyperbolic space

- Mathematics
- 2020

The one-loop effects to the Dirac action of $p$-branes in a hyperbolic background from the path integral and the solution of the Wheeler-DeWitt equation are analysed. The objective of comparing the…

Wilson loops for non-Abelian T duality and matrix models

- Mathematics
- 2021

We compute Euclidean Wilson loops for BMN Plane Wave Matrix Models by probing 1/2 BPS Type IIA geometries with F strings and D2 branes. These geometries fall under the general category of Lin and…

Nonlocal symmetries, spectral parameter and minimal surfaces in AdS/CFT

- Mathematics, Physics
- 2017

M2-doughnuts

- Mathematics, PhysicsJournal of High Energy Physics
- 2022

Abstract
We present a family of new M2-brane solutions in AdS7× S4 that calculate toroidal BPS surface operators in the $$ \mathcal{N} $$
N
= (2, 0) theory. These observables are conformally…

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