Physical properties of W gravities and W strings

Abstract

We investigate some basic physical properties of W gravities and W strings, using a free field realization. We argue that the configuration space of W gravities have global characteristics in addition to the Euler characteristic. We identify one such global quantity to be a "monopole" charge and show how this charge appears in the exponents. The free energy would then involve a "θ" parameter. Using a BRST procedure we find all the physical states of W₃ and W₄ gravities, and show that physical operators are nonsingular composites of the screening charge operators. (The latter are not physical operators for N≥3.) For W strings we show how the W constraints lead to the emergence of a single (and not many) extra dimension coming from the W-gravity sector. By analyzing the resulting dispersion relations we find that both the lower and upper critical dimensions are lowered compared to ordinary two-dimensional gravity. The pure W gravity spectrum reveals an intriguing "numerological" connection with unitary minimal models coupled to ordinary gravity.