Analytic calculation of the 1-loop effective action for the O(N+1)-symmetric 2-dimensional nonlinear sigma-model
Abstract
Starting from the 2-dimensional nonlinear ?-model living on a lattice ? of lattice spacing a with action S[?]=-12??z???, ?(z)?SN we compute a manifestly covariant closed form expression for the Wilson effective action Seff[?] on a lattice of lattice spacing ã in a 1-loop approximation for a Gaussian choice of blockspin, where C?(x)?C?(x)/|C?(x)| fluctuates around ?(x). C is averaging of ?(z) over a block x. The limiting case of a ?-function is also considered. The result extends Polyakov which had furnished those contributions to the effective action which are of order lnã/a. The additional terms which remain finite as a?0 include corrections other than coupling constant renormalization: a current-current interaction and a contribution from an augmented Jacobian which has a field dependence of a different kind than S has. Particular attention is paid to Seff's domain of validity in field space. It turns out that Hasenfratz and Niedermayer's choice of a low value of the parameter ? which governs the width of the Gaussian is optimal also in this respect. © 2001 Elsevier Science B.V.
Más información
Título según WOS: | Analytic calculation of the 1-loop effective action for the O(N+1)-symmetric 2-dimensional nonlinear sigma-model |
Título según SCOPUS: | Analytic calculation of the 1-loop effective action for the O(N+1)-symmetric 2-dimensional nonlinear ?-model |
Título de la Revista: | NUCLEAR PHYSICS B |
Volumen: | 612 |
Número: | 3 |
Editorial: | ELSEVIER SCIENCE BV |
Fecha de publicación: | 2001 |
Página de inicio: | 413 |
Página final: | 445 |
Idioma: | English |
URL: | http://linkinghub.elsevier.com/retrieve/pii/S0550321301003509 |
DOI: |
10.1016/S0550-3213(01)00350-9 |
Notas: | ISI, SCOPUS |