States and quantum effects in the collective field theory of a deformed matrix model

Abstract

We derive an equation which gives the tree-level scattering amplitudes for tachyons in the black-hole background using the exact states of the collective field hamiltonian corresponding to a deformed matrix model recently proposed by Jevicki and Yoneya. Using directly the symmetry algebra we obtain an explicit expression for a class of amplitudes in the tree approximation. We also study the quantum effects in the corresponding collective field theory. In particular, we compute the ground-state energy and the free energy at finite temperature up to two loops, and the first quantum correction to the two-point function.