Holographic hadron masses in the language of quantum mechanics

Abstract

String theory’s holographic QCD duality makes predictions for hadron physics by building models that live in five-dimensional (5D) curved space. We show that finding the hadron mass spectrum in these models amounts to finding the eigenvalues of a one-dimensional differential equation identical in form to the Schrödinger equation. Changing the structure of the 5D curved space is equivalent to altering the potential in the Schrödinger equation, which in turn alters the hadron spectrum. We illustrate this concept with three holographic QCD models possessing exact analogs in basic quantum mechanics: the free particle, the infinite square well, and the harmonic oscillator. In addition to making aspects of holographic QCD accessible to undergraduate quantum mechanics students, this formulation can provide students with intuition for the meaning of curved space. This paper is intended primarily for high-energy theoretical physicists interested in involving undergraduates in their research, but is also a suitable introduction to holographic QCD for advanced undergraduates and beginning graduate students with basic knowledge of general relativity and classical field theory.