Hidden Symmetries of LargeNQCD

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Abstract
The new symmetry of the loop dynamics of QCD is found. This is a local SUSY δs = θβ(s), δθ = β(s) of the superloop field Xμ(s, θ) = xμ(s) + θψμ(s). The remarkable thing is, there is no einbein-gravitino on this theory, which makes it a 1D topological supergravity, or locally SUSY quantum mechanics. Using this symmetry, we derive the large Nc loop equation in momentum superloop space. Introducing as before the position operator X̂μ we argue that the superloop equation is equivalent to invariance of correlation functions of products of these operators with respect to certain quadrilinear transformation. As a consequence of this nonlinear symmetry, the coefficients of the Voiculesku expansion of the position operator satisfy recurrent equations. The generators of this symmetry are involved in the glueball spectrum, as it follows from the loop-loop correlation function equation. The correlation functions of external flavor currents in the background of constant flavor gauge field with finite density of topological charge in the chiral limit are also considered. We represent them as certain finite dimensional integrals in superspace, involving the Green's function, which is expressed in terms of X̂μ. The expansion in powers of external momenta k1, …, kn is calculable in terms of the above universal numbers in the Voiculesku expansion.
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