Minimal area surfaces in AdSn+1 and Wilson loops

He, Yifei; Huang, Changyu; Kruczenski, Martin

doi:10.1007/jhep02(2018)027

Minimal area surfaces in AdS_n+1 and Wilson loops

Journal Article · Mon Feb 05 00:00:00 EST 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep02(2018)027· OSTI ID:1505222

He, Yifei ^[1]; Huang, Changyu ^[2]; ^[2]

Purdue Univ., West Lafayette, IN (United States). Dept. of Physics and Astronomy; Purdue Univ., West Lafayette, IN (United States)
Purdue Univ., West Lafayette, IN (United States). Dept. of Physics and Astronomy

The AdS/CFT correspondence relates the expectation value of Wilson loops in N = 4 SYM to the area of minimal surfaces in AdS₅. In this paper we consider minimal area surfaces in generic Euclidean AdS_n+1 using the Pohlmeyer reduction in a similar way as we did previously in Euclidean AdS₃. As in that case, the main obstacle is to find the correct parameterization of the curve in terms of a conformal parameter. Once that is done, the boundary conditions for the Pohlmeyer fields are obtained in terms of conformal invariants of the curve. After solving the Pohlmeyer equations, the area can be expressed as a boundary integral involving a generalization of the conformal arc-length, curvature and torsion of the curve. Furthermore, one can introduce the λ-deformation symmetry of the contours by a simple change in the conformal invariants. This determines the λ-deformed contours in terms of the solution of a boundary linear problem. In fact the condition that all λ deformed contours are periodic can be used as an alternative to solving the Pohlmeyer equations and is equivalent to imposing the vanishing of an infinite set of conserved charges derived from integrability.

View Accepted Manuscript (DOE)

Research Organization:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0007884

OSTI ID:: 1505222

Alternate ID(s):: OSTI ID: 22739029

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2018; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Figure 1(p. 10)

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