QUANTUM STRING DYNAMICS IN THE CONFORMAL INVARIANT SL(2,R) WZWN BACKGROUND - ANTI-DE-SITTER SPACE WITH TORSION - ART. NO. 026001

We consider classical and quantum strings in the conformally invariant background corresponding to the SL(2,R) WZWN model. This background i s locally anti-de Sitter spacetime with non-vanishing torsion. Conform al invariance is expressed as the torsion being parallelizing. The pre cise effect of the conformal invariance on the dynamics of both circul ar and generic classical strings is extracted. In particular, the conf ormal invariance gives rise to a repulsive interaction of the string w ith the background which precisely cancels the dominant attractive ter m arising from gravity. We perform both semi-classical and canonical s tring quantization, in order to see the effect of the conformal invari ance of the background on the string mass spectrum. Both approaches yi eld that the high-mass states are governed by m similar to HN (N is an element of N-o, N ''large''), where m is the string mass and H is the Hubble constant. It follows that the level spacing grows proportional ly to N:d(m(2)alpha')/dN similar to N, while the string entropy goes l ike S similar to root m. Moreover, it follows that there is no Hagedor n temperature, so that the partition function is well defined at any p ositive temperature. All results are compared with the analogue result s in anti-de Sitter spacetime, which is a nonconformal invariant backg round. Conformal invariance simplifies the mathematics of the problem but the physics remains mainly unchanged. Differences between conforma l and non-conformal backgrounds only appear in the intermediate region of the string spectrum, but these differences are minor. For low and high masses, the string mass spectra in conformal and non-conformal ba ckgrounds are identical. Interestingly enough, conformal invariance fi xes the value of the spacetime curvature to be - 69/(26 alpha'). [S055 6-2821(98)00314-2].