T-duality for boundary-non-critical point-particle and string quantum mechanics

It is observed that some structures recently uncovered in the study of CalogeroSutherland models and anyons are close analogs of well-known structures of boundary conformal field theory. These examples of “boundary conformal quantum mechanics”, in spite of their apparent simplicity, have a rather reach structure, including some sort of T-duality, and could provide useful frameworks for testing general properties of boundary conformal theories. Of particular interest are the duality properties of anyons and Calogero-Sutherland particles in presence of boundary-violations of conformal invariance; these are here briefly analyzed leading to the conjecture of a general interconnection between (deformed) boundary conformal quantum mechanics, T-type duality, and (“exchange” or “exclusion”) exotic statistics. These results on the point-particle quantum-mechanics side are compared with recent results on the action of T-duality on open strings that satisfy conformal-invariance-violating boundary conditions. Moreover, it is observed that some of the special properties of anyon and Calogero-Sutherland quantum mechanics are also enjoyed by the M(atrix) quantum mechanics which has recently attracted considerable attention. To appear in the proceedings of Quantum Aspects of Gauge Theories, Supersymmetry and Unification, Neuchâtel, 18-23 September 1997.