Minimal Area Surfaces, Euclidean Wilson loops and Riemann Theta Functions

Wilson Loops and Minimal Surfaces

The AdS/CFT correspondence suggests that the Wilson loop of the large N gauge theory with N = 4 supersymmetry in 4 dimensions is described by a minimal surface in AdS5 × S5. We examine various aspects of this proposal, comparing gauge theory expectations with computations of minimal surfaces. There is a distinguished class of loops, which we call BPS loops, whose expectation values are free fro...

Riemann Surfaces and Theta Functions MAST 661G / MAST 837J

Computing Riemann theta functions

The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-)periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation are given. First, a formula is derived allowing the pointwise approximation of Riemann theta functions, with arbitrary, user-specified precision. This formula ...

Calibrated Surfaces and Supersymmetric Wilson Loops

We study the dual gravity description of supersymmetric Wilson loops whose expectation value is unity. They are described by calibrated surfaces that end on the boundary of anti de-Sitter space and are pseudo-holomorphic with respect to an almost complex structure on an eight-dimensional slice of AdS5 × S. The regularized area of these surfaces vanishes, in agreement with field theory non-renor...

Higher genus Riemann minimal surfaces

Even though the classification of genus zero, embedded minimal surfaces is not complete, W. H. Meeks J. Perez and A. Ros [14], [15], [16] have made progress concerning the question of the uniqueness of the Riemann examples in the class of genus zero embedded minimal surfaces which have an infinite number of ends. They conjecture in [15] that every embedded minimal surface of finite genus and wi...