A New Type of Loop Equations

Abstract

We derive a new form of loop equations for light-like Wilson loops. In bosonic theories those loop equations close only for straight light-like Wilson lines. In the case of N=1 in ten dimensions they close for any light-like Wilson loop. Upon dimensional reduction to N=4 SYM in four dimensions, these loops become exactly the chiral loops which can be evaluated semiclassically, in the strong coupling limit, by a minimal surface in anti de-Sitter space. We show that the AdS calculation satisfies those loop equations. We also find a new fermionic loop equation derived from the gauge theory fermionic equation of motion.

24 pages, LaTeX

References in corpus (5)

• Large N Field Theories, String Theory and Gravity
• Wilson loops in large N field theories
• Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
• Wilson Loops and Minimal Surfaces
• Supersymmetric Wilson Loops in IIB Matrix Model

Cited by in corpus (8)

• Wilson Loops in Large N Theories
• Loop Equations and bootstrap methods in the lattice
• Wilson Loop Renormalization Group Flows
• Yangian Symmetry of smooth Wilson Loops in N=4 super Yang-Mills Theory
• Exact Renormalization Group and Loop Equation
• Loop Equation and Exact Soft Anomalous Dimension in N=4 Super Yang-Mills
• Loop Equation in D=4, N=4 SYM and String Field Equation on AdS_5 \times S^5
• Towards a tensionless string field theory for the N=(2,0) CFT in d=6