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W∞ AND ANOMALIES OF SELF-DUAL EINSTEIN THEORIES
Journal article   Peer reviewed

W∞ AND ANOMALIES OF SELF-DUAL EINSTEIN THEORIES

V. G. J Rodgers
Modern physics letters A, Vol.6(20), pp.1893-1900
06/28/1991
DOI: 10.1142/S0217732391002049
url
https://arxiv.org/pdf/hep-th/9203068View
Open Access

Abstract

Recently it has been demonstrated that self-dual Einstein Euclidean instantons possess an infinite-dimensional group of symmetries which contain the standard w∞. Since w∞ has a central extension only in its w2 subalgebra one may claim that there is an anomaly in the symmetry group of these instantons which is described by a 3-dimensional w2 effective action. Thus one has a bosonization of the 3/2 spin anomaly of the Eguchi–Hanson instantons. In analogy to w∞ we construct the 3-dimensional effective action for the Lone Star W∞ algebra. This suggests that there is a quantum deformation of the instantons that contributes to the effective action of 4-dimensional self-dual gravity. We comment on this possibility.

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