Dynamics on AdS2 and Enlargement of SL(2, R) to

We consider the enhancement of SL(2, R) to Virasoro algebra in a system ofN particles on AdS2. We restrict our discussion to the case of non-interacting particles, and argue that they must be treated as fermions. We find operators Ln whose commutators on the ground state, |vac〉, satisfy relations that are reminisent of c = 1 Virasoro algebra, provided N ≥ n ≥ −N . Same relations hold also on the states L−k|vac〉 , if (N−k) ≥ n ≥ −(N−k). The conditions Ln = L−n, and Lk|vac〉 = 0 for k ≥ 1, are also satisfied. ∗E-mail: [email protected]