On gauge fields - strings duality as an integrable system

Details On gauge fields - strings duality as an integrable system On gauge fields - strings duality as an integrable system

2000-04-14

arxiv.org/abs/hep-th/0004105v2

Phys.Lett. A275 (2000) 260-273

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1016/S0375-9601(00)00534-X

It was suggested in hep-th/0002106, that semiclassically, a partition function of a string theory in the 5 dimensional constant negative curvature space with a boundary condition at the absolute satisfy the loop equation with respect to varying the boundary condition, and thus the partition function of the string gives the expectation value of a Wilson loop in the 4 dimensional QCD. In the paper, we present the geometrical framework, which reveals that the equations of motion of such string theory are integrable, in the sense that they can be written via a Lax pair with a spectral parameter. We also show, that the issue of the loop equation rests solely on the properly posing the boundary condition.

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