(8,0) Quantum mechanics and symmetry enhancement in type I' superstrings

TL;DR

This paper investigates how quantum mechanics and symmetry enhancement phenomena occur in type I' superstring theory, revealing mechanisms behind gauge symmetry enhancements and their relation to D-brane configurations and dualities.

Contribution

It provides a detailed analysis of D-particle quantum mechanics in type I' backgrounds, elucidating symmetry enhancement mechanisms and their connection to brane configurations and dualities.

Findings

Enhanced gauge symmetries like E8 and E7 are realized at strong coupling.

Symmetry enhancements correspond to coincident D8-branes and orientifold planes.

The s-rule is derived from the Pauli exclusion principle via dualities.

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 $SO(14) \times U(1)$ to $E_8$ and $SO(12)\times U(1)$ to $E_7$ at strong type I' coupling. Enhancement to higher-rank groups involves both orientifold planes. For example, the enhanced $E_8 \times E_8 \times SU(2)$ 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.