A New Type of Loop Equations

TL;DR

This paper introduces a novel form of loop equations for light-like Wilson loops, demonstrating their closure properties in various theories and connecting them to minimal surfaces in AdS space, with new fermionic loop equations derived.

Contribution

It derives new loop equations for light-like Wilson loops, including fermionic equations, and shows their consistency with AdS/CFT calculations in N=4 SYM.

Findings

Loop equations close for straight light-like Wilson lines in bosonic theories.

In N=1 ten-dimensional theories, loop equations close for any light-like Wilson loop.

AdS calculations satisfy the derived 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.