One-loop finiteness of the four-dimensional Donaldson-Nair-Schiff non-linear sigma-model

TL;DR

This paper constructs a four-dimensional non-linear sigma-model, showing that imposing one-loop UV-finiteness conditions uniquely determines a potentially finite quantum theory analogous to the 2D Wess-Zumino-Novikov-Witten model.

Contribution

It introduces the most general 4D non-linear sigma-model with second-order derivatives and demonstrates that one-loop finiteness conditions uniquely specify a model with all-order finiteness potential.

Findings

The model is uniquely determined by one-loop UV-finiteness conditions.

It generalizes the 2D Wess-Zumino-Novikov-Witten model to four dimensions.

The model exhibits properties suggesting all-order quantum finiteness.

Abstract

The most general four-dimensional non-linear sigma-model, having the second-order 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 may be finite to all orders of the quantum perturbation theory. This model is known as 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.