4.4 Article

Topological lattice actions

Journal

JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 12, Pages -

Publisher

SPRINGER
DOI: 10.1007/JHEP12(2010)020

Keywords

Field Theories in Lower Dimensions; Nonperturbative Effects; Lattice Quantum Field Theory; Sigma Models

Funding

  1. Schweizerischer National-fonds (SNF)
  2. Innovations- und Kooperationsprojekt C-13 of the Schweizerische Universitatskonferenz (SUK/CRUS)

Ask authors/readers for more resources

We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not have the correct classical continuum limit and they cannot be treated using perturbation theory, but they still yield the correct quantum continuum limit. To show this, we present analytic studies of the 1-d O(2) and O(3) model, as well as Monte Carlo simulations of the 2-d O(3) model using topological lattice actions. Some topological actions obey and others violate a lattice Schwarz inequality between the action and the topological charge Q. Irrespective of this, in the 2-d O(3) model the topological susceptibility chi(t) = < Q(2)>/V is logarithmically divergent in the continuum limit. Still, at non-zero distance the correlator of the topological charge density has a finite continuum limit which is consistent with analytic predictions. Our study shows explicitly that some classically important features of an action are irrelevant for reaching the correct quantum continuum limit.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.4
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

No Data Available
No Data Available