This week

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.

The oldest and best established Swampland constraint is perhaps the idea that there are no global symmetries in quantum gravity. Traditionally, this idea has been regarded as not strong enough to strong constraints at low energies, since the quantum gravity symmetry breaking effects could be extremely weak. I will describe recent progress in Swampland, in conjunction with developments in generalized and non-invertible symmetries, which have led to the discovery of new branes in string theory, new mechanisms to engineer small couplings in string theory, and even ruling out some effective field theories in higher dimensions.

Thin enough black strings are unstable to growing ripples along their length, eventually pinching and forming a naked singularity on the horizon. We investigate how string theory can resolve this singularity. First, we study the string-scale version of the static non-uniform black strings that branch off at the instability threshold: "string-ball strings", which are linearly extended, self-gravitating configurations of string balls obtained in the Horowitz-Polchinski (HP) approach to near-Hagedorn string states. We construct non-uniform HP strings in spatial dimensions d≤6 and show that, as the inhomogeneity increases, they approach localized HP balls. We also examine the thermodynamic properties of the different phases in the canonical and microcanonical ensembles. We find that, for a sufficiently small mass, the uniform HP string will be stable and not evolve into a non-uniform or localized configuration. Building on these results and independent evidence from the evolution of the black string instability with α' corrections, we propose that, at least in d=4,5, string theory slows and eventually halts the pinching evolution at a classically stable stringy neck. In d≥6 this transition is likely to occur into a puffed-up string ball. The system then enters a slower phase in which the neck gradually evaporates into radiation. We discuss this scenario as a framework for understanding how string theory resolves the formation of naked singularities.