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Dimensional Reduction and the Yang-Mills Vacuum State in 2+1 Dimensions · Around

2007

Dimensional Reduction and the Yang-Mills Vacuum State in 2+1 Dimensions

Greensite, J., Olejnik, S.

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We propose an approximation to the ground state of Yang-Mills theory, quantized in temporal gauge and 2+1 dimensions, which satisfies the Yang-Mills Schrodinger equation in both the free-field limit, and in a strong-field zero mode limit.

Our proposal contains a single parameter with dimensions of mass; confinement via dimensional reduction is obtained if this parameter is non-zero, and a non-zero value appears to be energetically preferred.
A method for numerical simulation of this vacuum state is developed.
It is shown that if the mass parameter is fixed from the known string tension in 2+1 dimensions, the resulting mass gap deduced from the vacuum state agrees, to within a few percent, with known results for the mass gap obtained by standard lattice Monte Carlo methods.

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D. Diakonov, private communication

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A. Agarwal, D. Karabali and V. P. Nair, arXiv:0705.0394 [hep-th]

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