THE HAGEDORN TRANSITION AND THE MATRIX MODEL FOR STRINGS

We use the matrix formalism to investigate what happens to strings abo ve the Hagedorn temperature. We show that it is not a limiting tempera ture but a temperature at which the continuum string picture breaks do wn. We study a collection of N D-0-branes arranged to form a string ha ving N units of light-cone momentum. We find that at high temperatures the favored phase is one where the string worldsheet has disappeared and the low-energy degrees of freedom consists of N-2 massless particl es (''gluons''). The nature of the transition is very similar to the d econfinement transition in large-N Yang-Mills theories.