A Classical Manifestation of the Pauli Exclusion Principle

TL;DR

This paper demonstrates how the Pauli exclusion principle manifests in M-theory through the geometric properties of holomorphic curves representing fermionic states between branes, highlighting the absence of multiply-occupied states.

Contribution

It provides a geometric realization of the Pauli exclusion principle in M-theory by linking fermionic state occupancy to the existence of specific holomorphic curves.

Findings

Absence of multiply-occupied fermionic states corresponds to no suitable holomorphic curves.

Stable non-BPS states are represented by non-holomorphic curves.

The geometric approach illustrates fundamental quantum principles in string theory context.

Abstract

The occupied and unoccupied fermionic BPS quantum states of a type-IIA string stretched between a D6-brane and an orthogonal D2-brane are described in M-theory by two particular holomorphic curves embedded in a Kaluza-Klein monopole. The absence of multiply-occupied fermionic states --- the Pauli exclusion principle --- is manifested in M-theory by the absence of any other holomorphic curves satisfying the necessary boundary conditions. Stable, non-BPS states with multiple strings joining the D6-brane and D2-brane are described M-theoretically by non-holomorphic curves.