Quantum mechanics and symmetry enhancement in type I ’ superstrings

The low-energy supersymmetric quantum mechanics describing D-particles in the background of D8-branes and orientifold planes is analyzed in detail, including a careful discussion of Gauss’ law and normal ordering of operators. This elucidates the mechanism that binds Dparticles to an orientifold plane, in accordance with the predictions of heterotic/type I duality. The ocurrence of enhanced symmetries associated with massless bound states of a D-particle with one orientifold plane is illustrated by the enhancement of SO(14) × U(1) to E8 and SO(12)×U(1) to E7 at strong type I’ coupling. Enhancement to higher-rank groups involves both orientifold planes. For example, the enhanced E8×E8×SU(2) symmetry at the self-dual radius of the heterotic string is seen as the result of two D8-branes coinciding midway between the orientifold planes, while the enhanced SU(18) symmetry results from the coincidence of all sixteen D8-branes and SO(34) when they also coincide with an orientifold plane. As a separate by-product, the s-rule of brane-engineered gauge theories is derived by relating it through a chain of dualities to the Pauli exclusion principle.