Species Quantum Mechanics

TL;DR

This paper introduces concepts of Species Quantum Mechanics, exploring quantum operators related to species number and mass scale, and connects these ideas to moduli space quantization and black hole quantization in string theory.

Contribution

It proposes a novel framework for Species Quantum Mechanics, linking it to moduli space quantum mechanics and black hole quantization, and discusses the CRV pattern as a consequence of canonical commutation rules.

Findings

CRV pattern arises from canonical commutation rules

Connections established between species quantum operators and Calabi-Yau periods

Potential links to black hole quantization procedures

Abstract

In this note we introduce some concepts of Species Quantum Mechanics. Specifically, we consider quantum operators that correspond to the species number $N_s$ and the tower mass scale $m_t$ in the context of the swampland distance conjecture. We discuss the commutation relations, a possible wave function, and symplectic duality transformations on the conjugate variables. Furthermore, we argue that the Castellano-Ruiz-Valenzuela (CRV) pattern is a consequence of the canonical commutation rules of moduli space quantum mechanics. We also connect the canonical quantization to the periods of ${\cal N}=2$ Calabi-Yau compactifications to explore other aspects of the CRV pattern, including its possible connection to the Ooguri-Vafa-Verlinde black hole quantization procedure.