A New Type of Loop Equations

We derive a new form of loop equations for light-like Wilson loops. In bosonic theories those loop equations close only for straight lightlike 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.