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.

We discuss some physical aspects of W gravities and W strings. We identify global characteristics in W gravities (in addition to the usual Euler characteristic) and show how the dependence of the partition function on the various chemical potentials involves these quantities. We find the operators which create physical states in W3 and W4 gravities and discuss their relationship with screening operators. W strings are discussed in the framework of a natural way of coupling “matter” to W gravity, and the issues of extra dimensions and critical dimensions are clarified. We find a remarkable relationship between pure W gravities and ordinary gravity coupled to c<1 unitary minimal models.

D dimensional neutral black strings wrapped on a circle are related to (D − 1) dimensional charged black holes by boosts. We show that the boost has to be performed in the covering space and the boosted coordinate has to be compactified on a circle with a Lorentz contracted radius. Using this fact we show that the transition between Schwarzschild black holes to black p-branes observed recently in M theory is the well-known black hole-black string transition viewed in a boosted frame. In a similar way the correspondence point where an excited string state goes over to a neutral black hole is mapped exactly to the correspondence point for black p-branes. In terms of the p brane quantities the equation of state for an excited string state becomes identical to that of a 3 + 1 dimensional massless gas for all p. Finally, we show how boosts can be used to relate Hawking radiation rates. Using the known microscopic derivation of absorption by extremal 3-branes and near-extremal 5D holes with three large charges we provide a microscopic derivation of absorption of 0-branes by seven and five dimensional Schwarzschild black holes in a certain regime.

The question of how infalling matter in a pure state forms a Schwarzschild black hole that appears to be at non-zero temperature is discussed in the context of the AdS/CFT connection. It is argued that the phenomenon of self-thermalization in non-linear (chaotic) systems can be invoked to explain how the boundary theory, initially at zero temperature self thermalizes and acquires a finite temperature. Yang-Mills theory is known to be chaotic (classically) and the imaginary part of the gluon self-energy (damping rate of the gluon plasma) is expected to give the Lyapunov exponent. We explain how the imaginary part would arise in the corresponding supergravity calculation due to absorption at the horizon of the black hole.

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.