A Pedagogical Introduction to Holographic Hadrons

TL;DR

This paper explains how holographic QCD models predict hadron spectra by solving a Schrödinger equation in curved space, making the complex theory accessible through familiar quantum mechanics analogs.

Contribution

It provides a pedagogical framework linking holographic QCD to basic quantum mechanics models, aiding understanding for students and researchers.

Findings

Illustrates holographic QCD with quantum mechanics analogs

Shows how space structure affects hadron spectra

Provides educational tools for undergraduates

Abstract

String theory's holographic QCD duality makes predictions for hadron physics by building models that live in five-dimensional (5D) curved space. In this pedagogical note, we explain how finding the hadron mass spectrum in these models amounts to finding the eigenvalues of a time-independent, one-dimensional Schroedinger equation. Changing the structure of the 5D curved space is equivalent to altering the potential in the Schroedinger 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 undergraduates, this formulation can provide students with intuition for the meaning of curved space. This paper is intended primarily as a tool for researchers interested in involving early-stage undergraduates in research, but is also a suitable introduction to elements of holographic QCD for advanced undergraduate- and beginning graduate students with some knowledge of general relativity and classical field theory.