TODA FIELD-THEORIES ASSOCIATED WITH HYPERBOLIC KAC-MOODY ALGEBRA - PAINLEVE PROPERTIES AND W ALGEBRAS

We show that the Painleve test is useful not only for probing (non)int egrability but also for finding the values of spins of conserved curre nts (W currents) in Toda field theories (TFT's). In the case of TFT's based on simple Lie algebras the locations of resonances are shown to give precisely the spins of conserved W currents. We apply this test t o TFT's based strictly on hyperbolic Kac-Moody algebras and show that there exist no resonance other than that at n = 2, which corresponds t o the energy-momentum tensor, indicating their nonintegrability. We al so check by direct calculation that there are no spin-3 or -4 conserve d currents for all the hyperbolic TFT's in agreement with the result o f our Painleve analysis.