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

TL;DR

This work derives a microscopic, gauge-invariant quantum-mechanical description of D-particles in type I' backgrounds with D8-branes and orientifolds, treating Gauss' law and operator ordering to reveal binding to orientifold planes and consequent symmetry enhancements. Through a chain of dualities to heterotic/type I and a detailed analysis of bound states, it explains massless bound states responsible for enlarging gauge symmetry (e.g., $SO(14)\times U(1)\to E_8$, $SO(12)\times U(1)\to E_7$) and extends to higher-rank enhancements such as $E_8\times E_8\times SU(2)$, $SU(18)$, and $SO(34)$. It also derives the s-rule from fermionic Pauli-principle constraints in the bound-state sector and presents an exact mass-spectrum mapping $g m_I = a_I/(2r_{11})$, linking the I' quantum mechanics to the heterotic cylinder. The analysis emphasizes moduli-space connectivity, showing enhancements occur at boundary loci of a single moduli-space cover and discussing how winding and mirror sectors can realize otherwise inaccessible enhancements, thereby unifying brane dynamics with dual string descriptions.

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.