(8,0) Quantum mechanics and symmetry enhancement in type I' superstrings
Abstract
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 D-particles 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
E
8
and
SO(12)×U(1)
to
E
7
at strong type I' coupling. Enhancement to higher-rank groups involves both orientifold planes. For example, the enhanced
E
8
×
E
8
×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.