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Title:
Vacuum energy, contact term and all that in gauge systems with nontrivial holonony
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Abstract:
I present few highly nontrivial features of the gauge theories when the configurations with nontrivial holonomy play the crucial role in dynamics. First example is the computation of the contact term in a weakly coupled gauge theory, the so-called "deformed QCD". I argue that the configurations with nontrivial holonomy saturate the contact term which was conjectured for strongly coupled QCD long ago by Witten and Veneziano. Second example is computations of the contact term in nontrivial curved hyperbolic background. I argue that correction to the energy is linear in inverse size of the system L^{-1}. The correction is expressed in terms of gauge invariant holonomy, but can not be formulated in terms of local operators. It might be the key element in understanding of the observed cosmological dark energy, which is interpreted in this framework as the modification of the QCD vacuum energy in topologically nontrivial background.
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