Calibrated Surfaces and Supersymmetric Wilson Loops

TL;DR

This paper explores the gravity duals of supersymmetric Wilson loops with expectation value one, showing they are represented by calibrated, pseudo-holomorphic surfaces with zero regularized area, aligning with field theory non-renormalization theorems.

Contribution

It introduces a geometric description of supersymmetric Wilson loops via calibrated surfaces in AdS_5 x S^5, linking their properties to complex geometry and non-renormalization.

Findings

Calibrated surfaces end on the boundary of AdS_5 x S^5.

Regularized area of these surfaces vanishes.

Results agree with non-renormalization theorems in field theory.

Abstract

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 AdS_5 x S^5. The regularized area of these surfaces vanishes, in agreement with field theory non-renormalization theorems for the corresponding operators.