Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Minimal area surfaces dual to Wilson loops and the Mathieu equation

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [2]
  1. Purdue Univ., West Lafayette, IN (United States); Purdue Univ, Dept Phys & Astron, 525 Northwestern Ave, W Lafayette, IN 47907 USA
  2. Purdue Univ., West Lafayette, IN (United States)
+ Show Author Affiliations
The AdS/CFT correspondence relates Wilson loops in N=4 SYM to minimal area surfaces in AdS 5 × S 5 space. Recently, a new approach to study minimal area surfaces in AdS 3 c AdS 5 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 area surface can be computed analytically in terms of eigenvalues of such equation. As opposed to previous examples, these minimal surfaces have an umbilical point (where the principal curvatures are equal) and are invariant under λ-deformations. In various limits they reduce to the single and multiple wound circular Wilson loop and to the regular light-like polygons studied by Alday and Maldacena. In this last limit, the periodic potential becomes a series of deep wells each related to a light-like segment. Small corrections are described by a tight-binding approximation. In the circular limit they are well approximated by an expansion developed by A. Dekel. In the particular case of no umbilical points they reduce to a previous solution proposed by J. Toledo. The construction works both in Euclidean and Minkowski signature of AdS 3.
Research Organization:
Purdue Univ., West Lafayette, IN (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Grant/Contract Number:
SC0007884
OSTI ID:
1437361
Alternate ID(s):
OSTI ID: 22610401
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 8 Vol. 2016; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

References (54)

Integrable Hamiltonian systems and interactions through quadratic constraints journal October 1976
Exact results for Wilson loops in arbitrary representations journal January 2014
Algebraic curves for long folded and circular winding strings in AdS 5 × S 5 journal February 2013
Precision calculation of 1/4-BPS Wilson loops in AdS5×S5 journal February 2016
Constant mean curvature surfaces in AdS 3 journal March 2010
Wilson loops and minimal surfaces beyond the wavy approximation journal March 2015
Space-like minimal surfaces in AdS × S journal April 2010
An operator product expansion for polygonal null Wilson loops journal April 2011
Algebraic curves for factorized string solutions journal April 2013
Toward precision holography with supersymmetric Wilson loops journal April 2016
The spectrum of excitations of holographic Wilson loops journal May 2011
Wilson loops and Riemann theta functions II journal May 2014
Generalized quark-antiquark potential at weak and strong coupling journal June 2011
An exact formula for the radiation of a moving quark in $\mathcal{N} = 4$ super Yang Mills journal June 2012
Pohlmeyer reduction and Darboux transformations in Euclidean worldsheet AdS 3 journal August 2012
General Leznov-Savelev solutions for Pohlmeyer reduced AdS5 minimal surfaces journal September 2011
From correlation functions to Wilson loops journal September 2011
Form factors at strong coupling via a Y-system journal November 2010
Yangian symmetry of smooth Wilson loops in $ \mathcal{N}=4 $ super Yang-Mills theory journal November 2013
Correlation function of circular Wilson loops at strong coupling journal November 2013
Wilson loops and minimal area surfaces in hyperbolic space journal November 2014
Euclidean Wilson loops and minimal area surfaces in lorentzian AdS 3 journal December 2015
Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops journal May 2012
Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity journal November 2001
A two-dimensional model for mesons journal June 1974
A planar diagram theory for strong interactions journal April 1974
Gauge theory correlators from non-critical string theory journal May 1998
Wilson loop correlator in the AdS/CFT correspondence journal July 1999
Wilson loops in supersymmetric Yang–Mills theory journal August 2000
Supersymmetric Wilson loops journal November 2002
Surprises in the AdS algebraic curve constructions — Wilson loops and correlation functions journal August 2012
Dressed Wilson loops on S2 journal August 2011
The Large-N Limit of Superconformal Field Theories and Supergravity journal January 1999
An exact prediction of N=4 supersymmetric Yang–Mills theory for string theory journal July 2001
A note on twist two operators in Script N = 4 SYM and Wilson loops in Minkowski signature journal December 2002
Spiky strings and single trace operators in gauge theories journal August 2005
On the integrability of Wilson loops in AdS 5 × S 5 : some periodic ansatze journal January 2006
On the Dynamics of finite-gap solutions in classical string theory journal July 2006
1/4 BPS circular loops, unstable world-sheet instantons and the matrix model journal September 2006
Gluon scattering amplitudes at strong coupling journal June 2007
Comments on gluon scattering amplitudes via AdS/CFT journal November 2007
Generating AdS string solutions journal March 2008
Supersymmetric Wilson loops on S 3 journal May 2008
Matching the circular Wilson loop with dual open string solution at 1-loop in strong coupling journal May 2008
Moduli dynamics of AdS 3 strings journal June 2009
Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space journal November 2009
Double-helix Wilson loops: case of two angular momenta journal December 2009
sinh-Gordon, cosh-Gordon, and Liouville equations for strings and multistrings in constant curvature spacetimes journal August 1996
Wilson Loops in Large N Field Theories journal June 1998
Spin Chains and String Theory journal October 2004
WAVY WILSON LINE AND AdS/CFT journal May 2005
PHASE TRANSITIONS IN WILSON LOOP CORRELATOR FROM INTEGRABILITY IN GLOBAL AdS journal January 2012
hyperbolic space journal October 1993
Anti de Sitter space and holography journal January 1998

Cited By (3)

Deformations of the circular Wilson loop and spectral (in)dependence journal January 2019
Minimal area surfaces in AdSn+1 and Wilson loops journal February 2018
Deformations of the circular Wilson loop and spectral (in)dependence text January 2018

Similar Records

Euclidean Wilson loops and minimal area surfaces in lorentzian AdS 3
Journal Article · Sun Dec 13 19:00:00 EST 2015 · Journal of High Energy Physics (Online) · OSTI ID:1437363
Minimal area surfaces in AdSn+1 and Wilson loops
Journal Article · Sun Feb 04 19:00:00 EST 2018 · Journal of High Energy Physics (Online) · OSTI ID:1505222
Wilson loops and minimal area surfaces in hyperbolic space
Journal Article · Thu Nov 13 19:00:00 EST 2014 · Journal of High Energy Physics (Online) · OSTI ID:1454534

Related Subjects

't Hooft and Polyakov loops
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AdS-CFT correspondence
Wilson