Week 24.02.2025 – 02.03.2025

Quantum Chromodynamics (QCD) has been a profound source of inspiration for theoretical physics, driving the development of key concepts such as string theory, effective field theories, instantons, anomalies, and lattice gauge theories. In these lectures, I will explore two distinct regimes of QCD - its infrared (IR) and ultraviolet (UV) limits - and the theoretical tools used to study them.

In the IR regime, where perturbative techniques break down, Effective Field Theories (EFTs) provide a powerful framework. I will introduce the pion EFT as a tool to study non-linearly realized symmetries and soft theorems. In the UV regime, where QCD becomes amenable to perturbative analysis, I will discuss the Operator Product Expansion and renormalization group equations, focusing on their application to deep inelastic scattering, a cornerstone in the discovery of quarks and gluons.

These two regimes illustrate the richness of QCD and its pivotal role in shaping our understanding of fundamental physics.

I explore decoupling limits that lead to matrix theories on D-branes, focusing on their BPS nature and the emergence of non-Lorentzian target space geometries. In these limits, D-branes experience instantaneous gravitational forces, and when applied to curved geometries, it is shown that a single decoupling limit leads to the AdS/CFT correspondence. By applying two such limits, we generate new holographic examples, including those with non-Lorentzian bulk geometries. I also discuss the relationship between matrix theories and non-relativistic string theory, and their uplift to M-theory. Finally, we demonstrate that reversing these decoupling limits connects to the TTbar deformation in two dimensions. This provides a new perspective on the near-horizon brane geometry and leads to TTbar-like flow equations for the Dp-brane DBI action.