New Special Operators in $W$-Gravity Theories

Details New Special Operators in $W$-Gravity Theories New Special Operators in $W$-Gravity Theories

1991-09-18

arxiv.org/abs/hep-th/9109028v1

Mod. Phys. Lett. A6 (1991) 3531-3542

Physics

High Energy Physics

High Energy Physics - Theory

15 pages

Scientific paper

We find new special physical operators of $W_3 -$gravity having non trivial ghost sectors. Some of these operators may be viewed as the liouville dressings of the energy operator of the Ising model coupled to {\it 2d~gravity} and this fills in a gap in the connection between pure $W_3 -$gravity and Ising model coupled to 2d gravity found in our previous work. We formulate a selection rule required for the calculation of correlators in $W -$gravity theories. Using this rule, we construct the non ghost part of the new operators of $W_N -$gravity and find that they represent the $(N , N+1)$ minimal model operators from both inside and outside the minimal table. Along the way we obtain the canonical spectrum of $W_N -$gravity for all $N$ .

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