All Loop Finiteness of the Four - Dimensional Donaldson - Nair - Schiff Non - Linear Sigma - Model 1

Abstract

The most general four-dimensional non-linear sigma-model, having the secondorder derivatives only and interacting with a background metric and an antisymmetric tensor field, is constructed. Despite its apparent non-renormalizability, just imposing the one-loop UV-finiteness conditions determines the unique model, which turns out to be finite to all orders of the quantum perturbation theory. This model appears to be the four-dimensional Donaldson-Nair-Schiff theory, which is a four-dimensional analogue of the standard two-dimensional Wess-Zumino-Novikov-Witten model, and whose unique finiteness properties and an infinite-dimensional current algebra have long been suspected. Supported by the ‘Volkswagen Stiftung’ 2 On leave of absence from: High Current Electronics Institute of the Russian Academy of Sciences, Siberian Branch, Akademichesky 4, Tomsk 634055, Russia

Cite this paper

@inproceedings{Ketov2008AllLF, title={All Loop Finiteness of the Four - Dimensional Donaldson - Nair - Schiff Non - Linear Sigma - Model 1}, author={Sergei Ketov}, year={2008} }