NEW SPECIAL OPERATORS IN W-GRAVITY THEORIES

We find new special physical operators of W3-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 two-dimensional (2D) gravity and this fills in the gap in the connection between pure W3-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 WN-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 WN-gravity for all N.