Effective sigma models and lattice Ward identities

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.

arXiv comment25 pages, 17 figures, JHEP style

References in corpus (22)

• Knots and Particles
• Partially Dual variables in SU(2) Yang-Mills Theory
• To be or knot to be?
• Faddeev-Hopf knots: Dynamics of linked un-knots
• An effective action for monopoles and knot solitons in Yang-Mills theory
• Yang-Mills theory as an Abelian theory without gauge fixing
• Aspects of Electric and Magnetic Variables in SU(2) Yang-Mills Theory
• Wilsonian effective action for SU(2) Yang-Mills theory with Cho-Faddeev-Niemi-Shabanov decomposition
• Glueball masses and other physical properties of SU(N) gauge theories in D=3+1: a review of lattice results for theorists
• Towards a string representation of infrared SU(2) Yang-Mills theory
• Magnetic monopole loop for the Yang-Mills instanton
• Classical Gauge Vacua as Knots
• On P-vortices and the Gribov problem
• Instantons and Gribov Copies in the Maximally Abelian Gauge
• Theory of Abelian Projection
• Magnetic monopoles vs. Hopf defects in the Laplacian (Abelian) gauge
• A lattice study of the Faddeev-Niemi effective action
• Remarks on the Gribov Problem in Direct Maximal Center Gauge
• Abelian projected SU(2) Yang-Mills action for renormalisation group flows
• Iterating Block Spin Transformations of the O(3) Non-Linear Sigma-Model
• Infrared Yang-Mills theory as a spin system. A lattice approach
• Demons and Abelian Projection QCD: Action and Crossover

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• Effective Lattice Actions for Finite-Temperature Yang-Mills Theory
• On Gauge Choice of Spherically Symmetric 3-Branes