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

TL;DR

This paper derives scattering amplitudes for tachyons in a black hole background using a deformed matrix model's collective field theory, and investigates quantum effects including energy, free energy, and correlation corrections.

Contribution

It provides explicit tree-level amplitudes and quantum corrections in the collective field theory of a deformed matrix model related to black hole physics.

Findings

Explicit tree-level tachyon scattering amplitudes derived

Quantum corrections to ground state energy and free energy computed

First quantum correction to the two-point function obtained

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 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.