Topological charge on the lattice: a field theoretical view of the geometrical approach

Abstract

We construct sequences of ``field theoretical'' (analytical) lattice topological charge density operators which formally approach geometrical definitions in 2-d $C{P}^{N-1}$ models and 4-d $SU(N)$ Yang Mills theories. The analysis of these sequences of operators suggests a new way of looking at the geometrical method, showing that geometrical charges can be interpreted as limits of sequences of field theoretical (analytical) operators. In perturbation theory renormalization effects formally tend to vanish along such sequences. But, since the perturbative expansion is asymptotic, this does not necessarily lead to well behaved geometrical limits. It indeed leaves open the possibility that non-perturbative renormalizations survive.

14 pages, revtex

References in corpus (7)

• Instantons and the fixed point topological charge in the two-dimensional O(3) sigma-model
• Renormalization and topological susceptibility on the lattice: SU(2) Yang-Mills theory
• Improved lattice operators: the case of the topological charge density
• Topological susceptibility and string tension in the lattice CP(N) models
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• Scaling topological charge in the CP^3 spin model
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Cited by in corpus (6)

• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Critical slowing down of topological modes
• Theta-dependence of the spectrum of SU(N) gauge theories
• Topological susceptibility from twisted mass fermions using spectral projectors and the gradient flow
• The Euclidean two-point correlation function of the topological charge density
• Worm Algorithm for CP(N-1) Model