Wilson loops and riemann theta functions in the gauge/gravity duality

Sannah Phi Ziama, Purdue University

Abstract

One important implication of the AdS/CFT conjecture is that the expectation value of a Wilson loop operator in a conformally invariant field theory may be computed in the dual string theory by calculating the regularized area of the minimal area surface that ends on the Wilson loop in the boundary of AdS space. As a consequence, Euclidean Wilson loops correspond to minimal area surfaces in Euclidean AdS space. Many examples of Euclidean Wilson loops have been computed including the parallel lines which give the quark-antiquark energy. We approach the study of Wilson loops from the point of view of finding Riemann theta function solution to the cosh-gordon equation. We compute an infinite set of equivalent classes of simple Wilson loops. Each equivalent class consists of Wilson loops that, though having different shapes and lengths, have the same regularized area of their dual minimal area surfaces. An analytic formula for the area of their dual surfaces is derived. Furthermore new examples of Wilson loops which consist of multiple curves are calculated. For instance we compute cases of concentric Wilson loops which may be viewed as perturbed concentric circular Wilson loops. The trace of their monodromy matrix which gives information about the conserved charges is determined to be a simple function of the spectral parameter.

Degree

Ph.D.

Advisors

Kruczenski, Purdue University.

Subject Area

Physics|Theoretical physics

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