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

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.

11 pages, LaTeX, macros included; revised version

References in corpus (3)

• N=4 Topological Strings
• Gso Projection, BRST Cohomology and Picture-Changing in N=2 String Theory
• The String Measure and Spectral Flow of Critical N=2 Strings

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