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 2d gravity and this fills in a 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 inW−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 . ⋆ e-mail : [email protected] Prefitem