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Jacob Goeree

Publications and source records attributed to Jacob Goeree.

5 recordsLinked to original sources
arXiv1992

The Effective Action of $W_3$ Gravity to All Orders

The effective action for chiral $W_3$ gravity is studied. It is shown that the computation of the effective action can be reduced to that of a $SL(3,\re)$ Wess-Zumino-Witten theory. If one assumes that the effective action for the Wess-Zumino-Witten model is identical to the WZW action up to multiplicative renormalizations, then the effective action for $W_3$ gravity is, to all orders, given by a constrained WZW model. The multiplicative renormalization constants of the WZW model are discussed and it is analyzed which particular values of these constants are consistent with previous one-loop calculations, and which reproduce the KPZ formulas for gravity and their generalizations for $W_3$ gravity.

hep-th↗
arXiv1992

KPZ Analysis for $W_3$ Gravity

Starting from the covariant action for $W_3$ gravity, we discuss the BRST quantization of $W_3$ gravity. Taking the chiral gauge the BRST charge has a natural interpretation in terms of the quantum Drinfeld--Sokolov reduction for $Sl(3,\re)$. Nilpotency of this charge leads to the KPZ formula for $W_3$. In the conformal gauge, where the covariant action reduces to a Toda action, the BRST charge is equivalent to the one recently constructed by Bershadsky et al.

hep-th↗
arXiv1992

Covariant $W$ Gravity \& its Moduli Space from Gauge Theory

In this paper we study arbitrary $W$ algebras related to embeddings of $sl_2$ in a Lie algebra $g$. We give a simple formula for all $W$ transformations, which will enable us to construct the covariant action for general $W$ gravity. It turns out that this covariant action is nothing but a Fourier transform of the WZW action. The same general formula provides a geometrical interpretation of $W$ transformations: they are just homotopy contractions of ordinary gauge transformations. This is used to argue that the moduli space relevant to $W$ gravity is part of the moduli space of $G$-bundles over a Riemann surface.

hep-th↗
arXiv1991

W Gravity From Chern--Simons Theory

Starting with three dimensional Chern--Simons theory with gauge group $Sl(N,R)$, we derive an action $S_{cov}$ invariant under both left and right $W_N$ transformations. We give an interpretation of $S_{cov}$ in terms of anomalies, and discuss its relation with Toda theory.

hep-th↗