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Euclidean Wilson loops and minimal area surfaces in lorentzian AdS 3

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2]
  1. Ivy Tech Community College, Lafayette, IN (United States); Purdue Univ., West Lafayette, IN (United States). Dept. of Physics and Astronomy; Ivy Tech Community Coll, Lafayette, IN 47905 USA
  2. Purdue Univ., West Lafayette, IN (United States). Dept. of Physics and Astronomy
+ Show Author Affiliations
The AdS/CFT correspondence relates Wilson loops in N=4 SYM theory to minimal area surfaces in AdS 5 × S 5 space. If the Wilson loop is Euclidean and confined to a plane (t, x) then the dual surface is Euclidean and lives in Lorentzian AdS 3 c AdS 5. In this paper we study such minimal area surfaces generalizing previous results obtained in the Euclidean case. Since the surfaces we consider have the topology of a disk, the holonomy of the flat current vanishes which is equivalent to the condition that a certain boundary Schrödinger equation has all its solutions anti-periodic. If the potential for that Schrödinger equation is found then reconstructing the surface and finding the area become simpler. In particular we write a formula for the Area in terms of the Schwarzian derivative of the contour. Finally an infinite parameter family of analytical solutions using Riemann Theta functions is described. In this case, both the area and the shape of the surface are given analytically and used to check the previous results.
Research Organization:
Ivy Tech Community College, Lafayette, IN (United States); Purdue Univ., West Lafayette, IN (United States)
Sponsoring Organization:
Indiana Dept. of Workforce Development (United States); National Science Foundation (NSF) (United States); USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Grant/Contract Number:
SC0007884
OSTI ID:
1437363
Alternate ID(s):
OSTI ID: 22587589
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2015; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

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