Quantum Chromodynamics (QCD) is our best description of strongly interacting particles called hadrons — the most familiar being protons and neutrons. According to QCD, hadrons are not fundamental: they are composed of quarks and gluons. Yet curiously, we cannot isolate a single quark or gluon. They always appear bound together inside a hadron. This peculiar property is called quark confinement.

Remarkably, theories closely related to QCD that exhibit confinement appear to be equivalent to a theory of strings living in one higher spatial dimension. This surprising equivalence is known as Gauge/Gravity duality, and it offers a powerful new lens for understanding confinement.

I have explored this duality numerically for toy models in which space is two-dimensional. In these models, the picture that emerges is striking: a fundamental string propagating in the higher-dimensional space appears, when viewed from the lower dimension, as a thick flux tube. The image is obtained by numerically solving for the QCD flux tube using a fundamental string in one higher spatial dimension.

The familiar matter around us is built from spin-half particles — electrons, quarks, and their kin. Quantum mechanics combined with special relativity yields a mathematically beautiful description of these particles through the Dirac equation. Following Feynman, one can also describe them using path-integrals, a formulation that reveals curious and subtle properties not immediately apparent from the wave-equation perspective.