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arXiv · hep-lat/0210021

Effective sigma models and lattice Ward identities

Leander Dittmann·Thomas Heinzl·Andreas Wipf
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Abstract

We perform a lattice analysis of the Faddeev-Niemi effective action conjectured to describe the low-energy sector of SU(2) Yang-Mills theory. To this end we generate an ensemble of unit vector fields ("color spins") n from the Wilson action. The ensemble does not show long-range order but exhibits a mass gap of the order of 1 GeV. From the distribution of color spins we reconstruct approximate effective actions by means of exact lattice Schwinger-Dyson and Ward identities ("inverse Monte Carlo"). We show that the generated ensemble cannot be recovered from a Faddeev-Niemi action, modified in a minimal way by adding an explicit symmetry-breaking term to avoid the appearance of Goldstone modes.

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Leander Dittmann, Thomas Heinzl, Andreas Wipf. 2002-10-14. Effective sigma models and lattice Ward identities. https://doi.org/10.1088/1126-6708%2F2002%2F12%2F014

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