Comparing Different Improvement Programs for the N-Vector Model

Abstract

We discuss the connection between various types of improved actions in the context of the two-dimensional sigma-model. We also discuss spectrum-improved actions showing that these actions do not have any improved behaviour. An O(a^2) on-shell improved action with all couplings defined on a plaquette and satisfying reflection positivity is also explicitly constructed.

Comments: We clarify that the discrepancy noted previuosly between the on-shell and the Symanzik programs is a pathology of the large N limit. ps file available also at http://www1.le.infn.it:8080/~caraccio/96.html